UC-NRLF 


2fl    DDE 


MODERN 

BUSINESS 

ARITHMETIC 


LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 


GIFT    OF 


Class 


4 


SWEET'S 

Modern  Business  Arithmetic 


A  TREATISE  ON 


MODLRN  AND  PRACTICAL  METHODS 


OF 


ARITHMETICAL  CALCULATIONS 


FOR  THL  USE.  OF 


Business  and  Commercial  Colleges,  Business  Universities, 

Commercial  High  Schools,  Technical  Schools,  and 

Commercial  Departments  in  Other  Ldu-] 

cational  Institutions 


BY 


Typography  by 

J.  5.  SWLLT  PUBLISHING  CO. 
Santa  Rosa.  Cal. 


Press  of 

1  908  THL  HICK5-JUDD  COMPANY 

San  Francisco,  Cal. 


Entered  according  to  Act  of  Congress,  in  the  year  1907 

By  J.  S.  SWEET,  A.  M. 

In  the  office  of  the  Librarian  of  Congress, 

at  Washington,  D.  C. 


ELECTROTYPED  BY 

FILMER  BROS.  ELECTROTYPE  CO. 

SAN  FRANCISCO,  CAL. 


Preface 


IFTER  thirty  years  experience  as  a  teacher  of 
mathematics,  the  author  feels  that  he  is  able 
to  present  the  subject  of  commercial  arith- 
metic to  students  and  instructors  in  a  man- 
ner which  is  not  only  severely  practical  and 
up  to  date,  but  attractive  and  intensely  interesting. 
No  claims  are  made  in  regard  to  the  discovery  of 
new   facts  in  the  science  of  arithmetic.     While  the 
manner   of  presenting   the  topics    to    the    class,    the 
method  of  illustration,   exemplification,   and  practice 
have  been  used  by  the  author  for  many  years,  no  pub- 
lished work  has  ever  been  issued  handling  the  science 
in  this  extremely  practical  manner. 

Particular  attention  is  called  to  the  different  parts 
into  which  the  work  is  divided.  "  Class  Work, " 
"HomeWork,"  "Test,"  and  "Final  Examinations," 
each  has  its  place  in  the  development  of  every  topic. 
The  topics  are  made  largely  independent  of  one  an- 
other, so  that  students  entering  school  at  different 
times  may  take  up  the  work  together.  This  will  be 
found  a  most  excellent  feature  in  business  college 
work.  A  system  of  credits  is  also  suggested  which 
will  spur  the  student  to  do  his  best  at  all  times. 


23656 


To  the  Teacher 

The  following  plan  of  preparation,  recitation,  test,   credits, 
and  examination  is  suggested  : 

I.  PREPARATION:     Students  should   be   assigned    certain 
definite  work  to  prepare  for  each  recitation.     Such  preparation 
should  be  made  before  coming  to  the  class  room. 

II.  RECITATION  :     Students  should  be  required  to  discuss 
each  topic  in  class  before  any  blackboard  demonstrations  are 
given.  "  Blackboard  examples,   fully  illustrated    and    discussed, 
should  bring  out  the  principles  of  each  topic.     Every  student 
should  be  required  to  solve  at  least  one  problem  in  each  subject 
and  discuss  it  from  the  board  before  the  class. 

III.  TESTS  :     Tests  may  be  given  at  the  close  of  each  sub- 
ject, or  may  be  postponed  for  two  weeks.     The  latter  method  is 
found  to  be  the  more  satisfactory,  as  it  compels  the  student  to 
review  the  subject. 

IV.  HOME  WORK  :     Twenty-five    different   exercises    for 
-Home    Work    have    been    carefully    prepared.      Each    student 

should  be  required  to  hand  in  a  correct  solution  of  these,   sys- 
tematically arranged,  as  a  part  of  his  permanent  record. 

V.  CREDITS  :     A  good  plan  in  recording  the  work  of  stu- 
dents is  to  divide  the  work  into  two  parts  :     Class  Work  and 
Home   Work.     Class  Work,    including   recitations,     demonstra- 
tions on  the  blackboard,  and  criticisms,  may  be  rated  on  a  basis 
of  100  credits,  the  credits  being  actually  earned  as  the  subjects 
are   passed.     Home  work  should  consist    of   the    papers    filed 
with  the  teacher,  and  may  be  given  100  credits,   an  average  of 
four  credits  for  each  paper.     Only  accurate,  neat,  and  tastefully 
arranged  work  should  be  given  credits.     This  work  should  be 
filed  away  for  future  reference. 

VI.  FINAL  EXAMINATIONS  :     Final  examinations  may  be 
given,  if  thought  advisable,  though  experience  has  taught  that 
with  the  above    system    carefully  carried  out  they  are    hardly 
necessary. 


To  the  Student 


You  are  about  to  begin  a  course  of  study  that  is  to  prepare 
you  for  the  active  duties  of  business.  As  you  succeed  here,  so 
will  your  teacher  and  those  about  you  judge  of  your  success  in 
the  real  battle  of  business.  Here  you  will  win  or  lose,  tfor  your 
school  life  is  but  the  epitome  of  your  future. 

Resolve,  then,  to  win.  Take  up  each  lesson  with  a  deter- 
mination to  master  it  from  start  to  finish.  Every  lesson  thor- 
oughly learned  will  make  those  coming  after  the  easier.  Test 
and  examination  will  then  become  a  pleasure  instead  of  a  dread, 
and  you  will  reap  an  abundant  reward. 

Post  yourself  thoroughly  upon  your  ' '  class  work ' '  by 
studying  the  definitions  and  discussions  of  each  topic,  and  by 
such  preparation  upon  the  examples  and  problems  as  will  enable 
you  to  recite  intellegently  and  correctly. 

The  "Home  Work"  should  be  prepared  at  home,  and 
should  be  carefully  arranged  on  your  paper  so  the  examiner  may 
note  the  method  of  solution  and  the  answer  at  a  glance.  Full 
credits  will  not  be  given  you  unless  the  above  is  carefully  ob- 
served. 

Please  note  the  plan  of  the  ' '  system  of  credits ' '  used  by 
your  teacher,  and  strive  to  reach  the  very  highest  point  possible. 
Success  is  yours  if  you  work  faithfully,  methodically,  and  per- 
sistently. 

RECORD  OF  CREDITS  : 


No. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

Cr. 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

NOTE — Should  the  student  .so  desire,    he  may  keep  a  record  of  his 
earned  credits  on  the  above  form. 


CONTENTS 

DEFINITIONS     .  7 

How  TO  WRITE  AND  READ  NUMBERS  -  8 

ADDITION                                            -  .                 -  13 

SUBTRACTION  .                 -  21 

MULTIPLICATION      -  -        -        -  25 

DIVISION  .        _  37 

PROPERTIES  OF  NUMBERS  -  41 

CANCELLATION  -                 -  47 

COMMON  FRACTIONS  49 

DECIMAL  FRACTIONS  53 

SIMPLE  INTEREST  73 

ALIQUOT  PARTS  77 

ANALYSIS  -  81 

BILLS,  INVOICES,  AND  STATEMENTS  88 

DENOMINATE  NUMBERS  95 

REDUCTION  OF  DENOMINATE  NUMBERS  -  109 

LONGITUDE  AND  TIME  -  121 

DENOMINATE  FRACTIONS  -  125 

AREAS,  SURFACES,  AND  VOLUMES  -  130 

PRACTICAL  MEASUREMENTS  -  140 

RATIO  AND  PROPORTION  -  147 

PERCENTAGE  -                         -  151 

PROFIT  AND  Loss  -  157 

TRADE  AND  CASH  DISCOUNTS  -  162 

COMMISSION  .  igg 

STOCKS  AND  BONDS  -  175^ 

TAXES     -  .  182' 

U.  S.  CUSTOMS  OR  DUTIES  -  184 

INSURANCE       -  -        -  188 

INTEREST                                          _  -        -  194 

COMPOUND  INTEREST      -  _  204 

COMMERCIAL  PAPER  -  207 

PARTIAL  PAYMENTS        -  -        -  217 

DISCOUNT                  --_._.  _  225 

BANKING  AND  EXCHANGE       -  -     .  -  228 

EQUATION  OF  PAYMENTS       *  -        -  -                 -  233 

STATEMENTS  AND  BALANCE  SHEETS  -  240 

PARTNERSHIP  -  945 

ANSWERS                    -  251 


Modern  Business  Arithmetic 


Definitions 

1.  A  Unit  is  a  single  thing  ;  as  one,  one  dollar,  one  dozen. 

2.  A  Number  is  one  or  more  units  taken  as  a  whole  ;  as 
one,  five,  two  cents,  fifty  feet. 

3.  An  Integer  is  a  number  representing  whole  things  ;  as 
six,  seven,  nine  men,  twenty  dollars. 

4.  A  Fraction  is  a  number  representing  parts  of  things  ; 
as  one-half,  two-thirds,  three- fourths  of  a  mile. 

5.  An  Even  Number  ends  in  0,  2,  4,  6,  or  8  ;  as  10,  32, 
54,  76,  98. 

6.  An  Odd  Number  ends  in  1,  3,  5,  7,  or  9  ;  as  11,  23, 
35,  47,  59. 

7.  An  Abstract  Number  is  the  number  itself  without 
reference  to  things  ;  as  7,  25,  142. 

8.  A  Concrete  Number  always  refers  to  some  particular 
thing ;  as  7  quarts,  25  cents,  14  desks,  50  men. 

9.  A  Denominate  Number  is  one  whose  unit  is  a  meas- 
ure ;  as  2  hours,  5  yards,  37  pounds. 

The  unit  of  these  numbers  is  the  hour,  yard,  and  pound. 

10.  A  Simple  Number  is  a  single  number  ;  as  four,  or  4 
feet, 

11.  A  Compound  Number  is  a  concrete  number  of  two  or 
more  denominations  ;  as  5  feet  6  inches,  or  2  gallons  3  quarts  1 
pint. 

12.  Lfike  Numbers  refer  to  the  same  kind  of  unit ;  as  3 
and  8,  2  dollars  and  30  dollars. 


8  :.i.)r.i':R\:Bps-^XE3S  ARITHMETIC 

13.  Unlike  Numbers  refer  to  different  kinds  of  units  ;  as 
3  dollars,  and  80  bushels;  5  hours,  and  10  boys. 

14.  Arithmetic  is  the  science  of  numbers  and  the  art  of 
computation. 

Science  is  the  amassed  knowledge  pertaining  to  a  subject. 

Art  is  the  power  or  skill  to  use  the  knowledge  embodied  in  a  science. 


How  to  Write  and  to  Read  Numbers 

15.  Figures  are  used  to  express  numbers;  the  ten  characters 
used  in  Arabic  notation  are  : 

1234567        89         0 

One,  Two,  Three,  Four,  Five,  Six,  Seven,  Eight,  Nine,  Naught. 

16.  A  number  consisting  of  only  one  figure  is  called  Units ; 
as  5,  indicates  5  units. 

17.  A  number  consisting  of  two  figures  contains   tens  and 
units;  as  45,  indicates  4  tens  and  5  units,   and  is  read  forty- 
five. 

"Forty"  is  a  contraction  of  "four  tens." 

-  18.  A  number  consisting  of  three  figures  contains  hun- 
dreds, tens,  and  units;  as  345,  indicates  3  hundreds,  4  tens, 
and  5  units,  and  is  read  three  hundred  forty -five. 

19.  If  the  ' '  0  "  occurs  in  a  number  it  is  not  read  as  it  has 
no  value  ;  thus,  305  is  read  three  hundred  five ;  740  is  read  seven 
hundred  forty. 

20.  Numbers  consisting  of  more  than  three  figures  are  sepa- 
rated into  periods  of  three  figures  each,  beginning  at  the  right. 
Each  period  is  named  as  follows : 


10,  999,  888,  777,  666,  555,  444,  333,  222,  111,  567,  234. 

21.  Bach  period  is  read  as-  standing  alone,  then  its  name  is 
given;  as:  421,672,305  is  read  "four  hundred  twenty-one 
million,  six  hundred  seventy-two  thousand ',  three  hundred  five. 


NOTATION    AND    NUMERATION  9 

Since  units  is  the  name  of  the  last  period  and  always  a  part  of  the 
number  read,  its  name  is  not  used. 

22.     Copy  and  read  the  following  : 

/ 


7 


7 


L?  >-  /    ^  s^-  ^    *,  f 

7,  £  ^  ^  r  J~  tf,  7  ^  ^ 


23.  Write  the  following  in  figures  on  the  blackboard  : 

1.  Eighty-  four. 

2.  Six  hundred  eighty. 

3.  Four  hundred  nine. 

4.  Two  thousand,  five  hundred  ten. 

5.  Fifty  thousand,  twenty. 

6.  Seventy-five  million,  two  thousand,  four. 

7  .  Nine  hundred  trillion,  seven  billion,  two  hundred. 

8.  Two  million,  two  thousand,  two  hundred  two. 

9.  One  hundred  billion,  ten  million,  one. 

10.  Thirty    quadrillion,    three   hundred    three    million,   two 
hundred  three. 

NOTE  —  From  the  above  it  will  be  noticed  that  the  word   "and"  is 
omitted  when  writing  or  reading  whole  numbers. 


10 


MODERN    BUSINESS    ARITHMETIC 


Roman  Method  of  Writing  Numbers 

24.     In  Roman  Notation  seven  capital  letters  are  used  in 
writing  numbers,  as  follows  : 

I       V       X       L       C          D  M 


One        Five 


Ten 


Fifty         One  Five  One 

Hundred    Hundred    Thousand 


25.  Principles  of  Roman  notation  : 

1.     Repeating    a    letter   repeats  its  value,   as:     II  is  two,    XXX   is 
thirty,  CCC  is  three  hundred. 

2.  A  letter  placed  after  one  of  greater  value  is  added  to  it ;  if  placed 
before,    is    subtracted    from   it ;    thus :   VI    is   six,    IV  is  four,    MC  is 
eleven  hundred,  CM  is  nine  hundred. 

3.  A  letter  placed  between  other  letters  is  subtracted  from  their  sum  ; 
thus  :     XIV  is  fourteen,  CIX  is  one  hundred  nine. 

4.  A  bar  placed  over  a  letter  multiplies  it  by_pne  thousand ;  a  double 
bar,  by  one  million ;  thus  :  X  is  ten  thousand,   X  is  ten  million. 

NOTE — Four  is  represented  on  clock  and  watch  dials  by  IIII ;  in  all 
other  places  by  IV. 

26.  Roman  and  Arabic  notation  : 


I             1 

XI 

11 

XXI            21- 

C                 100 

II                     2 

XII 

12 

XXX            30 

CC              200 

III                 3 

XIII 

13 

XL               40 

CCC           300 

IV  or  IIII    4 

XIV 

14 

L                 50 

CD             400 

V                   5 

XV 

15 

LX              60 

D                500 

VI                 6 

XVI 

16 

LXI             61 

DC              600 

VII               7 

XVII 

17 

LXXII         72 

M              1000 

VIII              8 

XVIII 

18 

LXXX         80 

V              5000 

IX                 9 

XIX 

19 

LXXXVI     86 

XV          15000 

X                 10 

XX 

20 

XC              90 

L     50,000,000 

27.  Write  in  Roman  notation  : 

1.  Four. 

2.  Nine. 

3.  Thirteen. 

4.  Twenty- two. 

5.  Thirty-eight. 

6.  Forty-seven. 

7.  Sixty- four. 

8.  One  hundred  sixty-six. 

9.  Seven  hundred  ninety-nine. 
10.  Nineteen  hundred  seven. 


Also 


28 

74 

125" 

328 

972 

1,248 

27,853 

458,207 

2,576,324 

17,265,842 


NOTATION    AND    NUMERATION  11 

28.  Write  in  Arabic  notation  : 

1.  LXXXII.  6.  VmCDXIL 

2.  XLVII.  7.  XXXVDCCCLXXII. 

3.  DXII.  8.  DCCIIDCCCIJV. 

4.  DCCCXXIII.  9.  IVCCXXXVIDCCLn. 

5.  CCLXXIX.  10.  XXIVDCCCLVICCLXXI. 


HOME  WORK—  No.  1 

29.  Study  carefully  the  following  figures  and  practice  them 
thirty  minutes  every  evening  for  two  weeks,  then  hand  in  a  full 
page  of  your  best  work  : 


77777777777777777777 

?  f  f  f  f  r  r  r  f  ?  <r  r  &  r  r  r  <r  ^  ^  # 
?  7  7  7  77  7  ?  7  77  7  f  ?  7  ?  7  7  7  7 


j      j  * .  /  .t^  \    7     7       s  &- 

t>       7    <f   tf     &  /      2^-  ^J   */-  ^5 

7    (T   ^     0     /  ^~-  (J  ^  ^~  / 

?    #     /    ^^  *+^~    &     7    / 


/ 


12 


MODERN    BUSINESS    ARITHMETIC 


Outline  for  Review 


30.     Definitions : 

Unit.  9. 

Number.  10. 

Integer.  11. 

Fraction.  12. 

Even  number.  13. 

Odd  number.  14. 

Abstract  number.  15. 

Concrete  number.  16. 


1. 

2. 
3. 
4. 

5. 
6. 
7. 

8. 

1. 

2. 
3. 


Denominate  number. 
Simple  number. 
Compound  number. 
Like  numbers. 
Unlike  numbers. 
Arithmetic. 
Science. 
Art. 


Arabic  Notation  : 

Figures.  4.     Names  of  periods. 

Places  in  a  period.  5.     How  to  read  a  number. 

Names  of  places.  6.     How  to  write  numbers. 

Roman  Notation : 

Letters  used.  4.     How  to  read. 

Value  of  each.  5.     How  to  write. 

Principles  of  Roman  notation. 


ADDITION 

31.  Addition  is  the  process  of  finding  the  sum  of  two  or 
more  numbers. 

32.  The  Sum  is  the  result  obtained  by  addition. 

33.  The  Sign  of  Addition  is  +,  and  is  read  plus. 

34.  The  Sign  of  Equality  is  — ,  and  is  read  equals  ;  thus, 
4  +  5  =  9  is  read  four  plus  Jive  equals  nine. 

35.  PRINCIPLE — Only  like  numbers  can  be  added. 

36.  The  Sign  of  Dollars  is  $,  and  is  read  dollars.     When 
dollars  and  cents  are  expressed  a  period  separates  them ;  thus, 
$23.45  is  read  twenty -three  dollars  and  forty -five  cents. 

37.  The  sign  %  when  placed  before  a  number  is  read  num- 
ber, when  placed  after  a  number  is  read  pounds ;  thus,    #32  is 
read  number  thirty -two  ;  32  #  is  read  thirty -two  pounds. 

38.  Numbers  must  always  be  written  so  that  like  units  stand  in 
the  same  column.     Add  each  column  separately.     If  the  sum  of  any 
column  is  ten  or  more,  carry  the  tens  to  the  next  column. 


Reading  Method  of  Addition 

39.  There  are  but  forty -Jive  possible  combinations  of  the  nine 
digits  taken  two  at  a  time.     These  must  be  memorized  so  that 
when  any  one  of  the  combinations  is  seen  the  sum  is  instantly 
known.     The  combinations  are  as  follows  : 

40.  Sums  Less  Than  10  : 

/  /         ^  /          >-/         <J  *~  / 

—        *L       £l  ^£_        !r£_  f£        ^  *£~  <**- 
<J  >-  /  ^  ^  S-   /  ^  ^  3—  / 

^£^IA.      f±^l_^_7       <&  &  7   f 


14  MODERN    BUSINESS    ARITHMETIC 

41.    Sums  Greater  Than  9 : 
^r  ^  ^  ^  /  s^r-  -4^-  -Lr*  >  C-    ^  ^ 

£--£..  JL'JLjL  -t-LJl^L  A.^  IL 


42.  To  Read  at  Sight  : 

When  a  student  sees  the  numbers  1  and  3  written  side  by  side, 
he  instantly  knows  the  number  to  be  thirteen  or  thirty-one,  ac- 
cording to  their  positions. 

The  same  facility  may  be  acquired  in  addition  ;  thus  :  4  over 
or  under  8  may  be  read  twelve  as  readily  as  the  figures  1  and  2 
side  by  side. 

43.  Read  the  sums  of  two  figures  at  a  time.     Never  add  sin- 
gle  figures.     Name  the  result  of  the  following   as   rapidly   as 
possible  from  left  to  right,  from  right  to  left,  and  then  by  "skip- 
ping about : 


&_  j^\s_  ^£_^2  A_  7  _  f  f   >-  L/  ^  ^    ^    •/  <r  ^  <^ 


^r'r£±i:     __  _Z_  IL  jL.  ^     ± 


/- 


7  _/^  ^_  ^  _J?_   *£  ^_  _^_   7   ^_  j£_  ^  ^   ^  ^r_  _£_    7    _/^ 


ADDITION  15 

44.  Read  the  sums  of  the  following  grouping  the  figures  by 
twos;  thus,  in  the  left  hand  column  read  fifteen,  twenty -f our  ; 
in  the  next  column,  seven,  twenty-two,  etc.  : 

\j-£r<f~<^^>->^£    >  v*-  -v*  .^  /    ^  r  <^ 
^77  ^/   ^  /  ^  /"  /  ft  r  7  ^  /  *3  ? 
^77*  *  ?  f  r  ?  7  7  j  r  ?  t  *  7 


7  f    -      /-   7        '    <r  f 

&  ^  f7^-^<j~7^~^'f  j^  ^  ~^~  7   &  /"  4^ 
/   /  /    /  /  / 

*        7/7  '/ 

45.      To  Add  fry  Tens,  fifteens,  twenties,  thirties,  etc.,  carry 
the  excess  in  the  mind  as  in  the  following : 

v*-'    k>  7  r  7  r  /  ',JT  ;  .f  •>.":/ 

*-     s  *  *  t  *•  r            /  7      •*" 

r  <s  -s  s  7  f      7      s  t       * 

c.  7  t  s-  ^  (,       i.       j-  7       / 

X7  ^ 

7      v/       >-       7    -.••/-<        /        r       f       ^ 

f        f         7        *         f       7 
7       "       •*"      ^     /       * 

Many  times  it  is  convenient  to  add  the  figures  that  will  make 
even  &m  or  twenties,  etc.,  keeping  in  mind  the  unadded  digits 
until  they  will  unite  with  another  to  make  few  or  twenty  ;  thus  : 
in  the  right  hand  column  above  read  the  4  and  6,  7  and  3,  8  and 
2,  and  1  and  9  as  tens,  to  which  add  the  3  -f  4  ;  as  ten,  twenty, 
thirty,  forty -seven. 


16  MODERN    BUSINESS    ARITHMETIC 

46.  When  the  Columns  Are  I^ong,  add  each  column 
separately,  writing  the  sum  beneath,  then  add  results,  as  fol- 
lows : 


7 


t  ; 
r  > 
/ 


7 

7  1 
j>  /•  f 


ADDITION  17 

This  method  is  almost  indispensable  in  bookkeeping,  since  an 
error  can  be  detected  in  one  column  without  the  trouble  of  hav- 
ing to  add  all  the  others. 

47.  To  add  two  columns  at  a  time,  practice  on  the  following 
by  adding  the  tens'  column  first,  and  by  reading  the  units'  col- 
umn, tell  at  a  glance  the  number  to  carry  : 

2-   ^  <3    J~  6>     (,  \S   f  ^7  f    f^        -^7 


^   >         ^    /  c//-  7    y  ^    ^  y   ^~          f 

*  7      r  *      77      r  *       /:  7       ^7      7 


z^: 


48.  To  Prove  Addition,  add  the  second  time  down,  or 
up,  in  the  opposite  direction  of  the  first  addition.  In  short  col- 
umns, and  several  of  them,  the  addition  may  be  proved  by  cast- 
ing out  the  9's  as  shown  below  : 


/      <?     6 
/   ^$~    / 


Casting  out  the  9's  of  the  first  number,  we  have  an  excess  of  4; 
of  the  second,  6  ;  of  the  third,  5  ;  and  so  on  ;  finally  casting 
out  the  9's  of  these  results  gives  an  excess  of  4.  Then  casting 


18  MODERN    BUSINESS    ARITHMETIC 

out  the  9's  of  the  sum,  we  have  4,  which  agrees  with  the  former, 
indicating  the  probability  of  a  correct  addition. 

NOTE — This  is  not  always  a  sure  test ;  the  result  might  be  wrong,  and 
yet  prove  by  this  test. 

49.     Write  and  add  the  following  : 

/  ~J  s  <r  ^.^.^: 


j  ^r  /  .  t  c  r\r-£/.-*>  -J  /  7  "*  * 

<?   */  <$~  ,^Jt  f  <J*    lr    7   ^r  /-^  3~  -  ^  <? 

/  / 

&    7  <£  .  6~  ^5~  2^  f   <*£  £    f  j^ .  5    £ 

/  ^^ '                                                                                                                                                                                          '  / 

7^,r:v/7  //(,-//  ^^7  r  ,y  -J 

/  r,  /  J  (J  f  ^  >-  f  f  f  6  ,^? <S, 


<7 


/  7   r  r  ^  <r  >  ^  <r  /  77^ 


V   0   j£ 

r' 

^  f  7  ?  ^  7  ^  *  ?  r  _  / 

7  /    7  ,  r  *  ^s  7  t  *   * 

f  7  /  7^/-f/-/  **•**'  7  f  /./  <r 

r  f  7  p~<f.*'-f^'-/  f  ^  #  j.  ^-,  #<? 

/•  >  ^-  '&  /'s\&  -7-.?  &  *•  f  t.&  < 

7  /  x  ^  ^r  y  y  r  r  2-  ^  ^  *~  * 

>  /  j- _  ?  ?  >  ^-  '-*  ,<r  &  J  7  ^"  /• .  /-  ^ 


ADDITION  19 

PRACTICAL  PROBLEMS 

50.     Find  the  total  resources  of  each  of  the  following  per- 
sons : 

1.  L.  C.  BONDS:     Cash,   $11250;    Mdse.,  $28760.50;   Real 
Estate,  $65000  ;  Bank  Stock,  $15240  ;  Chattels,  $2185.75  ;  Good 
Will,   $5000;  Furniture  and  Fixtures,  $1844.25;  Bills  Receiv- 
able $848.20,   Interest  on  same,   $42.20;  Accounts  Receivable, 
$31245.85. 

2.  J.   M.  JOHNSON:     U.    S.    Bonds,    $40000;    Premium    on 
Same;  $6800,  Interest  on  Same,  $800  ;  Interest  in  Flour  Mills, 
$21245.50  ;   Mining  Stocks,  $2730  ;  Cattle  Ranch,  $8540  ;  Stock  : 
horses,  $1180;  cattle,  $4590;  sheep,  $2475.50;  Cash  in    bank, 
$3840.25;   Cash,  in  safe,  $573.25. 

3.  GEO.  H.  MOORE:     Cash   in   bank,   $7525.84;    Cash   on 
hand,     $1125.50;    Real    Estate,    $4200;     Factory     Equipment, 
$34237.50;  Water  Rights,  $5000;  Raw  Material  on  hand,   $52- 
372.25  ;  Manufactured  Goods  unsold,  $38576.75  ;  Insurance  pre- 
paid,   $735.60;    Chattels,   $2630.40;    Furniture   and  Fixtures, 
$1795. 

4.  L.  E.  ROOF:     Accounts  Receivable,  per  schedule   "A," 
$3196.75;  Real  Estate,  $45000;  Machinery,  $27000;  Mdse.,  per 
inventory,  $3113.92  ;  Furniture,  $457.20  ;  Rebate,  $895.91  ;  Silk 
and  Thread,  $212  ;   Traveling  Expenses,   unexpended,   $24.34; 
Cash  on   hand,   $8191.68;    Accounts  Receivable,   pen  schedule 
"B,"  less  50%  for  bad  debts,  $592.40  net. 

5.  FIRST  NATIONAL  BANK  :     Loans  and  Discounts,    $3320- 
699.50 ;  Overdrafts,  $5216  ;  U.  S.  Bonds,   to  secure  circulation, 
$152500;  U.  S.  Bonds  on  hand,  $126650;  Premiums  on  U.  S. 
Bonds,  $9695 ;  Banking  House  Furniture,   $12625 ;    Due  from 
other  banks,  $905168  ;  Checks  on  hand,   not  charged,  $18427  ; 
Exchanges  for  Clearing  House  on  hand,  $49895  ;  Bills  of  other 
National  Banks  on  hand,  $13595  ;  Fractional  Currency  on  hand, 
$984;  Gold  Coin  on  hand,  $188402  ;  Gold  Treasury  Certificates 
on   hand,    121275;    Silver  Dollars   on    hand,    $4800;    Clearing 
House  Certificates  on  hand,  $5000;  Silver  Treasury  Certificates 
on  hand,  $53648;  Legal  Tender  Notes  on  hand,   $470417;  Na- 
tional Bank  notes  (our  own  issue)  on  hand,   $14625  ;  Five  per- 
cent Redemption  Fund  with  United  States  Treasurer,  $6695. 


20 


MODERN  BUSINESS  ARITHMETIC 


HOME  WORK -No.  2 

NOTE — The  following  examples  are  to  be  copied  with  pen  and  ink  and 
should  represent  the  student's  best  work.  The  totals  may  be  written  in 
red  ink.  Prove  the  accuracy  of  the  work  by  casting  out  the  9's  : 


1. 

2. 

3. 

4. 

5. 

4298 

42805 

832165 

1273361 

315072683 

8215 

93176 

385601 

9164285 

509348716 

3156 

81524 

797615 

9273106 

816597338 

3548 

78165 

950872 

3827495 

509483726 

2167 

83495 

271345 

3816049 

379041748 

9245 

92750 

962876 

3150647. 

981506482 

3859 

28014 

170563 

2791586 

310743162 

5849 

50561 

508911 

3681325 

927483015 

8429 

71659 

381276 

5182497 

482497518 

8249 

28170 

428605 

9317653 

275109632 

1687 

80961 

428654 

1703975 

907158720 

6305 

30712 

135790 

2468013 

975310863 

1975 

86420 

284195 

3062591 

318098127 

4286 

75319 

812312 

5142338 

927661219 

9214 

42085 

321174 

3859271 

498372618 

3729 

43815 

461205 

4055842 

387267875 

5348 

27389 

843442 

7724259 

409892159 

3115 

93376 

422789 

2227498 

872262981 

6. 

7. 

8. 

9. 

10. 

1627 

50493 

271649 

2738113 

472916559 

2162 

94059 

837205 

1616227 

434227051 

7131 

40371 

478156 

3158219 

208849164 

9332 

29983 

516882 

9231586 

924716607 

3299 

58115 

932215 

3724190 

537961967 

2272 

52725 

238744 

3724057 

224274452 

4483 

73538 

264508 

1482472 

930882258 

4225 

55824 

166723 

5048321 

663727754 

7416 

49883 

922344 

7380996 

'434287661 

2243 

93265 

315068 

3246821 

428650286 

4287 

42897 

489322 

2260955 

999421682 

2766 

55944 

732915 

3629721 

192837508 

9382 

91327 

427994 

9543276 

883459277 

3721 

59047 

742236 

3489334 

248972214 

8294 

45893 

433997 

9327165 

973324598 

3184 

40751 

466158 

1086838 

571983349 

2974 

58158 

274894 

1468372 

905162792 

9383 

25941 

838832 

4398232 

384837929 

SUBTRACTION 

51.  Subtraction  is  the  process  of  finding  the  difference  be- 
tween two  numbers. 

52.  The  Minuend  is  the  greater  of  the  two  numbers. 

53.  The  Subtrahend  is  the  less  of  the  two  numbers. 

54.  The  Difference  is  the  result  obtained  by  subtraction. 

55.  The  Sign  of  Subtraction  is  — .     It  is   read  minus. 
When  placed  between  two  numbers  it  indicates  that  the  one  fol- 
lowing it  is  to  be  taken  from  the  one  before  it ;  thus,  14  —  6 
equals  8. 

56.  The  Sign  of  Equality  is  =.     When  placed  between 
two  numbers  or  sets  of  numbers  it  indicates  their  equality. 

57.  The  Parenthesis,  (  ),  and  Bar,  -       — ,  are  used  to 
indicate  numbers  considered    together ;  thus,  (5+8)  —  7  = 
9  —  6  —  3. 

58.  PRINCIPLE — Only  like  numbers  and   like  units  can  be 
subtracted. 

59.  PROOF — Add  the  subtrahend  to  the  difference.     The  sum 
should  equal  the  minuend. 

60.  If  the  subtrahend  figure  be  greater  than  that  of  the  minu- 
end, take  a  unit  from  the  next  higher  order  of  the  minuend,  and 
which  contains  ten  units  of  the  order  to  be  subtracted,   adding 
them  to  the  minuend  digit,  then  subtract  as  usual. 

3  10 

842 

Thus:  326     The  1  taken  from  the  4  adds  10  to  the  2. 
5  1  6. 


Reading  Method  of  Subtraction 

61.  When  the  forty-five  combinations  treated  of  in  ADDITION 
are  thoroughly  memorized,  the  process  of  subtraction  is  a  very 
simple  one.  This  consists  in  being  able  to  discern  at  a  glance 


22  MODERN    BUSINESS    ARITHMETIC 

the  number  which  will  combine  with  the  one  given  to  produce 
the  other.  Thus, 

<f     f    V     /       *      ?      r  .  /      i      f 

—         -^-^-2^-         —         J^^-_^L.2^  ^ 

are  given,  and  the  question  is  :  What  number  will  combine  with 
3  to  produce  8,  or  with  4  to  produce  9,  etc.?  The  process  is 
nearly  the  same  as  in  addition,  only  we  must  furnish  one  of  the 
numbers  to  the  combination,  the  result  being  known. 

62.     Read  the  differences  as  rapidly  as  possible  : 


/J         /  <S        ///  /c/  /^  /^  /f        /£  /f 

-*-    -?-    -^  ^7-  <?  -  _  f  _  /       /•  / 

/I        //       /J~  /£  //  /  /"  /.f../f  /  4- 

_  £l           7  7  ^  /"  _2       _  £.  /- 

7  /  ~  /~ 


f 


/:       <?        7       r       r 


8425 
3741 

68752 
34589 

27657 

1987  5 

41002 
37659 

45.321 

27184 

72318 
48921 

5283 
1694 

20875 
13796 

NOTE — To  become  expert  in  any  art,  it  is  necessary  to  practice  daily. 
Addition  and  subtraction  are  no  exceptions  to  this  rule.  The  processes 
set  forth  in  this  work  are  very  simple,  but  faithful,  persistent  practice 
only  will  perfect  and  give  value  to  them. 


SUBTRACTION  23 

63.     Find  the  differences  of  the  following  : 

*•    2-    f   /  (,     r    /    2~  p     2-    ^T    /  ^   S~  6     Z-  y     /     >  J7 


7     /       ^     ^  -7-**^ .     // 
<^    •J'    /---^  / 


PRACTICAI,  PROBI^^MS 

64.     Solve  the  following  : 

1.  I,.  Cush man's  total  assets  are  $9527.15;  his  liabilities  are 
$3645.85.     What  is  his  present  worth  ? 

2.  L,.  Ayers'  resources  amount  to  $17826.45  ;  his  outstanding 
indebtedness  is  $8245.50."     What  is  he  worth  ? 

3.  E.  L.  Payne  began  business  with  $2500,  borrowed  money. 
At  the  end  of  two  years  he  was  worth  $3528.50.     What  was  his 
gain  ? 

4.  M.  Coy  lost  $785.25  the  first  year  ;  gained  $255.75  the  sec- 
ond year,  when  his  present  worth  was  $5964.50.     What  was  his 
capital  at  the  beginning  ? 

5.  Brown  began  business  with  $1840.25  ;  the  first  year  he  lost 
$'280.50,  the  second  year  he  lost  $177.25,  the  third  year  he  gained 
$'.M;I  ».25,  the  fourth  year  he  lost  $128.40  ;     What  was  his  present 
worth  at  the  end  of  the  fifth  year  if  his  last  year's  gain  was  as 
much  as  his  total  losses  ? 


24  MODERN    BUSINESS    ARITHMETIC 

HOME  WORK— No.  3 

6.  J.  S.  Taylor  &  Co.s'  statement  at  the  close  of  the  year  was 
as  follows  :     Resources:  Mdse.  inventory,  $3585  ;  Cash,  in  bank, 
$2250;  Notes  on  hand,  $1275.50;  Accounts  Receivable,  $8960.25; 
Store  and  Lot,  $4500;  Furniture  and  Fixtures,  $1628.75;  Horses 
and  Wagons,  $785.40.     Liabilities:  Notes  Outstanding,  $2147.50; 
Interest  Payable,  $74.20;  Accounts  Payable,  $3487.25.    Find  the 
firm's  present  worth. 

7 .  The  following  statement  of  the  College  National  Bank  wras 
given  the  board  of  directors  :     Resources  :  Subscription,  $25000  ; 
U.  S.  Bonds,    $20000;    Cash  on  hand,    $21859.75;    Loans   and 
Discounts,    $43260;    N.   Y.    Bank,    $6729.50;    sundries    banks, 
$335.50.     Liabilities:  Capital  Stock,  $50,000;  Circulation,  $18- 
000;    Deposits,    $45064.10;    Business    College    Bank,    $482.50; 
Chemical  Bank,  $990  ;  College  Exchange  Bank,  $490  ;  Surplus 
Fund,  $396.82  ;  Dividends,  unpaid,  $500.     What  amount  should 
be  found  in  the  Undivided  Profits  Account  ? 

8.  K.  P.  Heald  and  F.  O.  Gardiner  became  partners  in  busi- 
ness with  the  following  resources  :     Cash,  $4000  ;   Mdse.,  $7850  ; 
Real  Estate,  $10000  ;  Bills  Receivable,  $5250  ;  Accounts  Receiv- 
able $12320. 40  ;  Interest  Receivable,  $782.50;  Furniture  and  Fix- 
tures,   $945;     Chattels,     $485.75.     Liabilities:     Bills    Payable, 
$675.25;  Interest  Payable,  $48.35;  Unpaid  Salaries  and  Rent, 
$286.80.     If  at  the  end  of  the  year  their  present  worth  is  $45- 
623.25,  what  is  their  gain? 

9.  A  milling  company's  present  worth  at  the  beginning  of 
the  year  is  $400000.     The  first  quarter  they  lose  $2432.85,   the 
second  quarter  they  gain  $8975.26,  the  third  quarter  they  gain 
as  much  as  their  net  gain  for  the  first  half  year,  the  last  quarter 
they  gain  as  much  as  in  the  second  and  third  quarters  ;  what  is 
their  present  worth  at  the  end  of  the  year  ? 

10.  The  resourses   of  the  First  National  Bank  are  given  on 
page  20.     If  the  liabilities  are  as  follows  :     Capital  Stock,  $500- 
000 ;    Deposits,    $3015485  ;    Surplus  Fund,    $125000  ;    National 
Bank  Notes  Issued,   $135485  ;    Due  to  other  National  Banks, 
$1269800 ;    Dividends   Unpaid,   $1176 ;    United  States  Deposits 
with  us,  $114697  ;  what  must  be  the  Undivided  Profits  ? 


MULTIPLICATION 

65.  Multiplication  is  a  short  method  of  making  additions 
of  the  same  number.     Thus,  5+5+5+5=4  times  5  =  20. 

66.  The  Multiplicand  is  the  number  to  be  repeated  or 
multiplied ;   as  5  in  the  above  example. 

67.  The  Multiplier  is  the  number  which  shows  how  many 
times  the  multiplicand  is  taken ;  as  4  in  the  above  example. 

68.  The   Product   is   the   result   obtained;    as    20   in  the 
above  example. 

69.  The  Sign  of  Multiplication  is  the  oblique  cross,    X  ; 
is  read  "times"  or  "multiplied  by."     Thus  3  times  8  is  writ- 
ten 3X8,  and  means  that  8  is  to  be  taken  or  added  to  itself 
three  times  and  equals  24. 

70.  The  multiplicand  and  the  multiplier  are  called  factors  of 
the  product. 

71.  An  Abstract  Number  is  the   number  itself  without 
reference  to  things  ;  as  5,  36,  240. 

72.  A  Concrete  Number  always  refers  to  some  particular 
thing  or  quantity  ;   as  12  hours,  80  miles,  500  horses. 

73.  The  multiplicand  may  be  either  abstract  or  concrete ;  the 
multiplier  is  always  considered  an  abstract  number;  the  product 
and  multiplicand  are  always  like  numbers.     Thus, 

5  times  7  =  35  ;  all  abstract  numbers. 
5  times  $7  =  $35  ;  multiplier  an  abstract  number,  the 
multiplicand  and  product  concrete  numbers. 

NOTE— In  computing  the  square  units  in  a  given  surface  where  the 
length  and  breadth  are  given,  the  product  of  these  two  dimensions 
equals  the  number  of  square  units  in  a  row  multiplied  by  the  number  of 
rows.  Thus,  instead  of  3  feet,  the  width,  times  4  feet,  the  length,  the 
analysis  is  3  times  the  4  square  feet  in  a  row,  or  12  square  feet. 


26 


MODERN    BUSINESS    ARITHMETIC 


74.     The  following  Multiplication  Table  should  be  thor- 
oughly memorized  before  proceeding  further  : 

MUI/TIPIylCATION  TABI,E 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

2 

4 

6 

8- 

10 

12 

14 

16 

18 

20   22 

24 

3 

6 

9 

12 

15 

18 

21 

24 

27- 

30 

33 

36 

4 

8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

5 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55 

60 

6 

12 

18 

24 

30 

36 

42 

48 

54 

60 

66 

72 

7 

14 

21 

28 

35 

42 

49 

56 

63 

70 

77 

84 

8 

16 

24 

32 

40 

48 

56 

64 

72 

80 

88 

96 

9 

18 

27 

36 

45 

54 

63 

72 

81 

90 

99 

103 

10 

20 

30 

40 

50 

60 

70 

80 

90 

100 

110 

120 

11 

22 

33 

44 

55 

66 

77 

88 

99 

110 

121 

132 

12 

24 

36 

48 

60 

72 

84 

96 

108 

120 

132 

144 

75.  A  Square  of  a  number  is  the  product  of  the  number 
multiplied  by  itself.     Thus,   25  is  the  square  of  5  ;   49    is   the 
square  of  7. 

76.  The  squares  of  all  numbers  up  to  30  should  also  be  mem- 
orized.    They  become  the  basis  of  further  knowledge  of  num- 
bers.    Thus : 


7 


/  f   - 


y 
yj.it 


MULTIPLICATION 


27 


77.  Alternating  Numbers  are  those  having,  in  their  reg- 
ular order,  a  number  between  them  ;  as,   5  and  7  ;   17  and   19 ; 
24  and  26. 

78.  The  Product  of  two  alternating  numbers  is  always  one 
less  than  the  square  of  the  intermediate  number.     Thus,  5  times 
7  ==  6  x  6  less  1  ;   17  times  19  =  18  X  1$  less  1. 

Solve  the  following : 


11  X  13 
12  X  14 
13  X  15 
14  X  16 

15  X  17 
16  X  18 
17  X  19 
19  X  21 

21  X  23 
22  X  24 
23  X  25 
24  X  26 

25  X  27 

26  X  28 
27  X  29 
29  X  31 

NOTE — The  product  of  two  numbers  having  three  intermediate  num- 
bers between  them  is  equal  to  the  square  of  the  central  number  less  4. 
Thus  8  times  12  equals  10  times  10,  less  4. 

79.  To  Multiply  a  Number  Consisting  of  Two  Dig- 
its by  11. 

Write  the  sum  of  the  digits  between  them;  the  number  thus  ex- 
pressed is  the  product. 

EXAMPLES  :     11  times  24  —  264.         11  times  47  =  517. 
11  times  32  =  352.          11  times  68  =  748. 

NOTE — When  the  sum  is  10  or  more,  carry  one  to  the  hundred's  digit. 
Solve  the  following : 


11  times  34 
11  times  43 
11  times  45 
11  times  44 
11  times  66 

11  times  38 
11  times  56 
11  times  71 
11  times  85 
11  times  79 

11  times  52 
11  times  65 
11  times  87 
11  times  69 
11  times  95 

11  times  75 
11  times  78 
11  times  88 
11  times  96 
11  times  99 

80.     To  Multiply  any  Number  by  11. 

Write  the  units  figure,  the  sum  of  the  units  and  tens,  the  sum  of 
the  tens  and  hundreds,  etc.,  also  the  left  hand  figure,  carrying  when 
necessary. 

EXAMPLE:     11  times  12345  =  f  5  5 


4  +  5  = 

9 

3  +  4  = 

7 

2  +  3  = 

5 

1  +  2- 

3 

-|                       

1 

135795 

28  MODERN    BUSINESS    ARITHMETIC 

Solve  the  following : 

1.  11  times  2134  6.     11  times  345281 

2.  11  times  4352  7.     11  times  587634 

3.  11  times  6217  8.     11  times  879605 

4.  11  times  7172  9.     11  times  378967 

5.  11  times  8154  10.     11  times  897968 
NOTE— To  Multiply  by  22,  33,  44,  etc.,  multiply  by  11  as   above, 

mentally,  then  by  2,  3,  4,  etc.,  in  the  same  operation. 

81.  To  Multiply  by  a  Single  Digit. 

Multiply  the  units  figure  of  the  multiplicand  by  the  multiplier, 
then  the  tens,  hundreds,  etc.  If  the  product  at  any  time  is  10  or 
more,  carry  the  tens  to  the  next  product ;  thus: 

24682 
4 

98728 

OPERATION  :     Four  times  2  —  8.     Four  times  8  =  32,   carry 
3.     Four  times  6  =  24,  +  3  =  27,   carry  2.     Four  times  4  - 
16,  +  2  =  18,  carry  1.     Four  times  2  =  8,  +1  =  9. 

Solve  the  following : 

1.  38751  X  3  =  ?  6.  55786  X  7  =  ? 

2.  25684  X  2  =  ?  7.  38972  X  8  =  ? 

3.  62753  X  4  =  ?  8.  45876  X  9  =  ? 

4.  29759  X  5  =  ?  9.  82975  X  4  =  ? 

5.  34287  X  6  =  ?  10.  88753  X  6  =  ? 

82.  To  Multiply  by  any  Number. 

Multiply  by  the  units  digit  as  above,  then  by  the  tens,  then  by  the 
hundreds,  etc.,  placing  the  full  product  by  each  digit  one  place  to  the 
left  of  the  one  bejore  it,  then  take  the  sum  of  the  several  products  ; 
thusy 

24682  =  multiplicand 

2354  =  multiplier 
98728  =  product  by  4 
123410     =  product  by  5 
74046        =  product  by  3 
49364  =  product  by  2 

58101428  =  TOTAL  PRODUCT. 

NOTE — To  Prove  Multiplication  by  casting  out  the  9's  : 
(1).  Cast  out  the  9's  of  the  multiplicand  and  also  of  the  multiplier. 
(2).  Cast  out  the  9's  from  the  product  of  the  remainders.     This  re- 
mainder should  equal  the  remainder  after  casting  out  the  9's  of  the  total 
product. 


MULTIPLICATION  29 

Solve  the  following  and  prove  : 


1. 

3845 

X 

2625 

=  ? 

6. 

83214 

X 

33654 

2. 

8227 

X 

3144 

=  ? 

7. 

77558 

X 

24875 

3. 

6782 

X 

4372 

=  ? 

8. 

84923 

X 

71684 

4. 

9247 

X 

5428 

=  ? 

9. 

98059 

X 

39563 

5. 

6782 

X 

6534 

=  ? 

10. 

56789 

X 

40387 

83.  To  Multiply  by  any  Number  between  12  and  2  0. 

Multiply  by  the  units  figure  only ;  write  the  result  under  the 
number  and  one  place  to  the  right,  then  add. 

EXAMPLE  :     13  times  235  =  (235 

<     705  =  3  times  235 

(3055. 
Solve  the  following : 

1.  312  X  13  =  ?  6.  14256  X  14  =  ? 

2.  425  X  14  =  ?  7.  26754  X  16  =  ? 

3.  565  X  15  =  ?  8.  30875  X  17  =  ? 

4.  364  X  16  =  ?  9.  59874  X  18  =  ? 

5.  721  X  17  =  ?  10.  78395  X  19  =  ? 

84.  To  Multiply  by  21,  31,  41,  51,  etc. 

Multiply  by  the  tens  figure  only,  writing  the  result  under  the 
number  and  one  place  to  the  left,  then  add. 

EXAMPLE  :     31  times  423  =  423 

1  269     =  3  times  423 
13113. 

Solve  the  following : 

1.  243  X  21  ==  ?  6.  724  X  41  ==  ? 

2.  325  X  31  =  ?  7.  785  X  61  =  ? 

3.  472  X  41  =  ?  8.  847  X  71  =  ? 

4.  537  X  51  =  ?  9.  875  X  81  =  ? 

5.  654  X  61  =  ?  10.  987  X  91  =  ? 

85.  To  Multiply  by  15. 

Anex  a  cipher  to  the  number  and  add  its  half. 

EXAMPLE  :     15  times  28  =  (  2  8  0  one  cipher  anexed 

<  140  =  \  of  280 
(420. 


30  MODERN    BUSINESS    ARITHMETIC 

Solve  the  following : 

1.  24  X  15  =  ?  6.  274  X  15  =  ? 

2.  36  X  15  =  ?  7.  482  X  15  =  ? 

3.  44  X  15  =  ?  8.  925  X  15  =  ? 

4.  54  X  15  =  ?  9.  896  X  15  =  ? 

5.  85  X  15  =  ?  10.  987  X  15  =  ? 

87.  To  Multiply  by  51. 

Take   one-half  the  number,  write  it  two  places  to  the  left  and  add. 

EXAMPLE  :     51  X  72  =      (         72 

<   36        =  \  of  72 
'   3672 

Solve  the  following : 

1.  48  X  51  =  ?  6.  324  X  51  =  ? 

2.  54X51  =  ?  7.  468X51  =  ? 

3.  66  X  51  =  ?  8.  525  X  51  =  ? 

4.  82  X  51  =  ?  9.  728  X  51  =  ? 

5.  95  X  51  =  ?  10.  895  X  51  =  ? 

88.  To  Find  the  Product  of  Complementary  Num- 
bers. 

Multiply  the  tens'  digit  by  one  unit  greater  and  annex  the  product 
of  the  units. 

NOTE — Complementary  Numbers  are  those  whose  tens'  digits  are 
identical  and  the  sum  of  whose  units'  digits  is  10. 

EXAMPLE  :     23  times  27  =  621. 

2X(2  +  1)=:6,  and  annex  3X7=  621. 

Solve  the  following : 

1.  14  X  16  =  ?  6.  52  X  58  =  ? 

2.  13  X  17  =  ?  7.  67  X  63  =  ? 

3.  26  X  24  =  ?  8.  74  X  76  =  ? 

4.  39  X  31  =  ?  9.  85  X  85  =  ? 

5.  45  x  45  =  ?  10.  93  X  97  =  ? 

89.  To  Find  the  Product  of  Two  Numbers  whose 
Units'  Digits  are  5's. 

To  the  product  of  the  tens  add  one-half  their  sum  in  whole  num- 
bers ;  if  the  sum  be  even,  annex  25  ;  if  odd ,  annex  75. 

EXAMPLE  :     25  times  45  =  2  X  4  +  ^^  ==  11 
Annex  25  =  1125. 


MULTIPLICATION  31 

EXAMPLE  :      35  times  65  =  3  X  6  +  L±J5  =  22 

Annex  75  =  2275. 
Solve  the  following : 

1.  25  X  65  =  ?  6.  35  X  55  =  ? 

2.  35  X  55  =  ?  7.  25  X  75  =  ? 

3.  45  X  85  =  ?  8.  45  X  95  =  ? 

4.  65  X  45  =  ?  9.  55  X  85  =  ? 

5.  75  X  95  =  ?  10.  75  X  95  =  ? 

90.  To  Find  the  Product  of  Two  Numbers  having 
a  Repeated  Digit  in  the  Multiplicand,  in  the  Multi- 
plier, or  in  the  Tens'  or  Units'  Place. 

Thus : 

33      alike  in  54    alike  in 

42  multiplicand  22  multiplier 

1386  1188 

47     alike  in  36      alike  in 

42  tens'  place  56  units'  place 

1974  2016 

Take  the  product  of  the  units,  the  product  of  the  like  digit  times 
the  sum  of  the  unlike  digits,  and  the  product  of  the  tens,  carrying 
when  necessary. 

EXAMPLE  :     52  times  44. 

4X2  8  product  of  units. 

4  X  (5  +  2)  =    28    product  of  the  like  dig- 
it times  the  sum  of  the 
unlike  digits. 
5X4  =20      product  of  the  tens. 

2288 
EXAMPLE  :     45  times  42 . 

2X5=        10  product  of  units. 

4X7=    28    product  of  like  digit  times  the 

sum  of  unlike  digits. 
4X4  ==  16      product  of  tens. 
1890 
NOTE — This  work  should  all  be  mental,  answers  only  to  be  written. 


32  MODERN    BUSINESS    ARITHMETIC 

Solve  the  following : 

1.  22  X  71  ==  ?  6.  82  X  83  =  ? 

2.  45  X  66  =  ?  7.  78  X  48  =  ? 

3.  34  X  37  =  ?  8.  63  X  65  =  ? 

4.  55  X  28  =  ?  9.  49  X  79  =  ? 

5.  46  X  36  =  ?  10.  85  X  86  =  ? 

91.  To  Find   the  Product  of  any  Two  Numbers 
Consisting  of  Two  Digits. 

.  Take  the  product  of  the  units,  the  sum  of  each  ten  times  the  other 
number's  unit,  and  the  product  of  the  tens,  carrying  when  necessary. 

EXAMPLE  :     47  times  36. 

6X7=         42  product  of  units. 

(6  X  4)  -f-  (3  X  7)  =    45    sum  of  products  of  tens  and  units 
4X3  =  12      product  of  tens. 
1692 

Solve  the  following : 

1.  24  X  35  =  ?  6.  46  X  39  =  ? 

2.  52  X  46  =  ?  7.  52  X  47  ==  ? 

3.  71  X  84  =  ?  8.  63  X  81  .-=  ? 

4.  38  X  57  =  ?  9.  85  X  92  =  ? 

5.  63  X  49  =  ?  10.  93  X  47  =  ? 

92.  To  Multiply  by  Complements. 

From  either  number  subtract  the  complement  of  the  other  \  and 
annex  the  product  of  the  complements. 

NOTE — A  complement  of  a  number  is  100,  1000,  etc.,  less  the  number. 
Thus,  the  complement  of  97  is  3,  of  88  is  12,  of  996  is  4,  etc. 

EXAMPLE  :     94  complement  6 

97  complement  3 

18  product  of  complements 
91      =  94  —  3  or  97  —  6 
9118 

EXAMPLE  :     998  complement  2 

989  complement  11 

022  product  of  complements 
987  =  998  —  11  or  989  —  2 
987022 

NOTE — When  the  numbers  consist  of  three  digits,  the  product  of  the 
complements  requires  three  places,  as  022  above. 


MULTIPLICATION  33 

Solve  the  following : 

1.  92  X  87  =  ?  6.  996  X  995  =  ? 

2.  94  X  75  =  ?  7.  975  X  994  =  ? 

3.  99  X  93  =  ?  8.  988  X  997  =  ? 

4.  97  X  91  ==  ?  9.  994  X  998  =  ? 

5.  88  X  95  =  ?  10,  999  X  989  =  ? 

93.  To  Multiply  by  Excesses. 

From  the  sum  of  the  numbers  subtract  100  or  1000,  as  required, 
and  annex  the  product  of  the  excesses. 

NOTE — An  excess  is  the  amount  greater  than  100,  1000,  etc. 

EXAMPLE  :     115  times  104  ==  11960. 
115  +  04  =  119 
To  119  annex  15  times  4  =.60  =  11960. 

EXAMPLE  :     1008  times  1007  =  1015056. 

1008  +  007  =  1015,  annex  056  =  1015056. 

Solve  the  following  : 

1.  1005  X  1007  =  ?  6.  1012  X  1005  =  ? 

2.  1004  X  1008  =  ?  7.  1015  X  1004  =  ? 

3.  1003  X  1009  =  ?  8.  1025  X  1002  =  ? 

4.  1002  X  1004  =  ?  9.  1035  X  1006  =  ? 

5.  1007  X  1009  =  ?  10.  1012  X  1025  =  ? 

NOTE — This  principle  may  be  carried  to  numbers  a  little  over  200, 
300,  400,  2000,  3000,  etc. 

94.  To  Find  the  Product  of  Two  Numbers,  one  of 
which  is  More  and  the  other  I/ess  than  100, 1000,  etc. 

From  the  sum  of  the  numbers  subtract  100  or  1000,  as  required, 
annex  two  ciphers  and  subtract  the  product  of  the  excess  and  com- 
plement. 

EXAMPLE  :     108  excess  8 
98  comp.  2 

10600 

Ifi  —  product  of  excess  and  comp. 

10584 
Solve  the  following : 

1.  102  X  94  ==  ?  6.  1004  X  992  =  ? 

2.  103  X  97  =  ?  7.  1008  X  995  =  ? 

3.  115  X  96  =  ?  8.  1015  X  993  =  ? 

4.  125  X  92  =  ?  9.  1025  X  994  =  ? 

5.  116  X  95  =  ?  10.  1075  X  998  =  ? 


34  MODERN    BUSINESS    ARITHMETIC 

PRACTICAL,  PROBLEMS 

95.     Solve  the  following- : 

1.  If  I  receive  $1800  salary,  pay  $260  for  board,  $187.50  for 
clothing,  $135.75  for  books,  $45.50  for  charity,  and  $105.25  for 
other  expenses  anually,  what  can  I  save  in  five  years  ? 

2.  A  merchant  bought  17  bolts  of  calico  at  4  cents  per  yard,  12 
bolts  sheeting  at  7  cents  per  yard,  21  bolts  silesia  at  8  cents  per 
yard,  and   14  bolts  cambric  at  3  cents  per  yard.     If  the  bolts 
contained  43  yards  each,  what  was  the  amount  of  the  bill  ? 

3.  Jones  paid  $1537.50  for  375  barrels  of  flour.     If  he  sold 
the  same  at  $4.35  per  barrel,  what  would  be  the  gain  ? 

4.  A  man  owing  $15760,  gave  in  payment  5  lots  of  land,  each 
worth  $730,  5  horses  valued  at  $236.50  each,   an  interest  in  a 
mine   worth   $2000,   and  $1728.75  in  money.     How  much  re- 
mained unpaid  ? 

5.  Bought  250  barrels  of  flour  for  $1150  ;  finding  25  barrels 
of  it  worthless,  sold  the  remainder  at  $4.75  per  barrel.     Did  I 
gain  or  lose,  and  how  much  ? 

6.  Brown's  inventory  of  stock  consisted  of  the  following : 
18  horses  worth  $75  each,    13   mules  worth  $52.50  each,   124 
milch   cows  worth  $41.25   each,   345  beef  steers  worth  $61.75 
each,  and  87  calves  worth  $7.50  each.     What  was  the  value  of 
his  stock  ? 

7.  Find  the  total  amount  of  the  following  inventory  :     7  bar- 
rels N.  O.  Molasses,  52,  53,  54,  45,  47,  49,  44,   @  35  cents  per 
gallon;    4  barrels  granulated  sugar,   325,   334,   328,   317,    @  5 
cents   per   Ib. ;    19  sacks  "A"   sugar,   100  Ibs.  to  the  sack,  @4 
cents  per  Ib. ;  5  bags  Rio  coif ee,  121,  128,  124,  131,  132,   @   19 
cents  per  Ib. 

8.  If  a  man  earns  $55  per  month  the  first  year,   $65  per 
month  the  second  year,  $75  per  month  the  third  year,  $85  per 
month  the  fourth  year,  and  $95  per  month  the  fifth  year ;  what 
will  be  his  earnings  for  the  whole  five  years  ? 

9 .  Smith  bought  bonds  as  follows  :   105  shares  Ohio  4 '  s  @  117, 
108  shares  of  Pensylvania  5's  @  113,  98  shares  N.  Y.  Central  @ 


MULTIPLICATION 


35 


92,  88  shares  of  Baltimore  &  Ohio  @  95,  112  shares  of  water 
bonds  @  98,  and  85  shares  of  Santa  Rosa  Municipal  4V s  @  105  ; 
what  was  his  total  investment  ? 

10.  Find  the  amount  of  the  following  bill  by  using  short 
methods  of  multiplication :  48  yards  of  cloth  @  11^,  34  yards 
@  22^,  45  yards  @  450,  62  yards  @  68^,  35  yards  @  37^,  84 
yards  @  54^,  65  yards  @  85^,  75  yards  @  45^,  36  yards 
72  yards 


1. 


HOME  WORK— No.  4 

Portland,  Oregon,     January   5 ,    1908 , 


MR.    C.    C.    DONOVAN, 

328  Fourth  Street 

Bought  of  A.  P.  ARMSTRONG  &  CO. 

—  DEALERS  IN  — 

Terms:    30   ds.  GRAIN,  HOPS  AND  FARM  PRODUCE 


42  bu.  Barley 

75 

24   »   Oats 

35 

18   "   Flax 

92 

76   "   Millet 

84 

225  "   Wheat 

95 

358  "   Corn 

55 

*** 

•** 

2.  Chicago,  111*,    February   10,  1908. 

MR.    0.    M.    POWERS, 
City 

Bought  of  N.  K.  FAIRBANK  &  CO. 

DEALERS  IN 

Terms:    60  ds. ,  5%  10  ds.          BEEF,  PORK,  FEED,  and  PRODUCE 


84  bbls.  Prime  Corned  Beef  12.— 
66   "    A  1  Salt  Pork     23.— 
720   "    XXX  R.  M.  Flour    6.— 
476  Sacks  Barley           .96 
7340#  Hazen  Cheese          .17 
1644#  Dairy  Butter          .30 
48  bbls.  N.  Y.  Salt         .98 

*** 

•*•* 

36 


MODERN    BUSINESS    ARITHMETIC 


3. 


R.    L.    GOODYEAR,    PRESIDENT 


L.    S.    GOODYEAR,    SEC.    TREAS. 


St.  I^ouis,  Mo.,  January  10,  1908. 
MR.  HARRISON  L.  MEYER, 

Memphis,  Tenn. 

BOUGHT  OF  THE  GOODYEAR   TEA    CO. 

Net  60  ds. 
TERMS:    5%  30  ds.  TEAS,  COFFEES,  and  SPICES 

10  %  10  ds. 


85  Ibs.  Fancy  "A"  Oolong      85c 
64  Ibs.  Choice      "        66c 
53  Ibs.  English  Breakfast     57c 
48  Ibs.  Choice  Blend         42c 
39  Ibs.  Fine  Black           31c 
75  Ibs.  Japan  Extra          75c 

9 

4. 


All  bills  due  subject  to  sight  draft 


E.  M.  Huntsinger  &  Company 

TEAS,  COFFEES,  COCOA,  AND  CHOCOLATE 

TERMS:    30ds.net  China  and  Glassware 

5  %  10  ds. 
SOLD  TO   W.  F.  PRICE  Hartford,  Conn.,    Mar.  4,    1908. 


135#  Old  Gov't  Java                         32c 
162#  Extra  Mocha                              35c 
147#  Costa  Rico                                 22c 
132#  Guatemala                                  23c 
144#  Salvador                                    18c 
152#  Vienna  Blend                             24c 

? 

5. 

O.   M.   BRIGGS,  PRESIDENT                                         ELWYN  SEA  TON,  SECRETARY                                         J.  S.  TAYLOR,  TREASURER 

If arin  ufark  Utanrit  Qlnmpang 

AGENTS  FOR 
GOLDEN   GATE  AND    NATIONAL  BISCUIT  COMPANIES 


BOOK  5,  Folio  #7 
SALESMAN  Smith 
TERMS  30  ds. 


CINCINATTI,  OHIO,  April  1,   1908, 
SOLD  TO    U.   S.  ARLAND,   Omaha,  Neb. 


132  Ibs.  American  Lunch       lie 
244  *  *  Cocoanut  Wafers      18c 
220  '  '  Chocolate  Wafers     22c 
230  '  '  Ginger  Snaps         14c 
260  *  *  Graham  Wafers        13c 
65   "  Pretzels           12c 
325  *  '   Sodas                9c 

9 

DIVISION 


96.  Division  is  the  process  of  ascertaining  how  many  times 
one  number  is  contained  in  another. 

97.  The  Dividend  is  the  number  divided. 

98.  The  Divisor  is  the  number  by  which  to  divide. 

99.  The  Quotient  is  the  result  obtained  by  division. 

100.  The  Remainder  is  the  number  left  after  dividing  when 
the  division  is  not  exact. 

101.  The  Sign   of  Division  is  •*-,  and  indicates  that  the 
number  before  it  is  to  be  divided  by  the  one  after  it. 

102.  PRINCIPLES  : 

1.  If  the  divisor  and  dividend  are  like  numbers,  the  quotient 
is  an  abstract  number. 

2.  If  the  divisor  is  an  abstract  number,  the  quotient  is  always 
like  the  dividend. 

3.  The  remainder  is  always  like  the  dividend. 

103.  PROOF  :     Multiply  the  quotient  by  the  divisor,  add  the 
remainder,  if  any,  and  the  result  should  equal  the  dividend. 

EXAMPLES  :     48  -^  4  ==  12. 

Proof,  4  times  12  =  48. 

56  -*-  9  =  6  and  2  remainder. 
Proof,  9  times  6  +  2  =  56. 


Short  Division 

104.     When  the  Operation  is  Performed  Mentally. 

Write  the  divisor  at  the  left  of  the  dividend  with  a  line  between. 
Divide  the  left  hand  digits  by  the  divisor  and  write  the  result  be- 
low. If  there  be  a  remainder  prefix  it  mentally  to  the  next  digit 
and  divide  as  before. 


38 


MODERN    BUSINESS    ARITHMETIC 


EXAMPLE  : 


215 

9  )  47846 


5316  and  2  remainder. 


OPERATION  :  47  -+-  9  =  5  and  2  remainder  ;  mentally  prefix 
2  to  the  next  figure,  and  28  -f-  9  =  3  and  1  remainder  ;  14  -*-  9 
=  1  and  5  remainder  ;  56  -?-  9  =  6  and  2  remainder. 

PROOF  :     9  times  5316  +  2  =  47846. 

NOTE  —  The  superior  figures  should  not  be  written,  but  wholly  carried 
in  the  mind. 


Solve  the  following : 


1. 
2. 

3. 
4. 
5. 


3426  -*-  3  =  ? 
4732  -s-  4  =  ? 
9678  -5-  2  =  ? 
8535  -s-  5  =  ? 
9122  -*-  6  =  ? 


6.  426713  -*-  7  =J 

7.  726645  -*-  8  =  ? 

8.  432756  -s-  9  =  ? 

9.  407301  -4-  6  =  ? 

10.  891530  -5-  7  =  ? 


I/ong  Division 

105.     When  the  Operations  are  Written. 

Write  the  divisor  at  the  left  of  the  dividend  with  a  line  between. 
Divide  as  in  mental  operations,  writing  the  figure  of  the  quotient  at 
the  right  or  above  the  dividend.  Multiply  the  divisor  by  the  quo- 
tient figure  and  subtract  the  product  from  the  left  hand  digits  of  the 
dividend.  Bring  down  the  next  figure  and  proceed  as  before. 

Thus  :     135  )  62352  (  461  quotient 
540 
835 
810 
252 
135 
117  remainder. 


Solve  the  following : 

1.  4272  -s-  16  =  ? 

2.  7175  -s-  25  =  ? 

3.  9676  -s-  34  =  ? 

4.  73521  -r-  40  =  ? 

5.  87965  -*-  57  =  ? 


6.  125789  -s-      61  =  ? 

7.  473826  •+•      79  —  ? 

8.  587634  •*•    145  =  ? 

9.  590430  -*-    470  =  ? 
10.  787945  -#•  1255  =  ? 


DIVISION  39 

106.     When  the  Divisor  Ends  in  Ciphers. 

Cut  off  as  many  figures  from  the  right  of  the  dividend  as  there 
are  ciphers  on  the  right  of  the  divisor,  and  divide  as  before.  The 
remainder  will  be  the  figures  cut  off  annexed  to  those  left  after  the 
last  subtraction. 

EXAMPLE  :     Divide  3576  by  400 

OPERATION  :     4,00  )  35,76 

8  and  376  remainder. 

Solve  the  following : 

1.  4500  -s-  30  =  ?  6.  75620  -*-      200  =  ? 

2.  7650  -5-  50  =  ?  7-.  89437  -*-      700  =  ? 

3.  3842  -4-  70  =  ?  8.  296753  •+•    3000  =  ? 

4.  9250-^80  =  ?  9.  576780 +-    8000  =  ? 
5  38520  -*-  90  =  ?  10.  5548237  -*-  90000  =  ? 


PRACTICAL  PROBLEMS 

107.     Solve  the  following  : 

1.  A  grocer  bought  two  kinds  of  syrup ;  one  for  54  cents  a 
gallon,  and  the  other  for  62  cents  a  gallon.     What  was  the  aver- 
age cost  a  gallon  ? 

2.  Hill's  sales  Monday  were  $104;  Tuesday,   $97;  Wednes- 
day,   $126;     Thursday,    $99;    Friday,    $142;    Saturday,   $120. 
What  wrere  his  average  daily  sales  for  the  week  ? 

3.  Frese  bought  140  acres  of  land  for  $7560,  and  sold  86  acres 
at  $75  per  acre,  and  the  remainder  at  cost.     How  much  did  he 
gain  ? 

4.  Jewett's  gain  the  first  year  was  $2140,  the  second  year  it 
was  double  the  first,  the  third  it  was  as  much  as  in  both  former 
years;  if  he  lost  $750  the  fourth  year,   and  gained  $1250  the 
fifth,  what  was  his  average  gain  per  year? 

5.  Olson  paid  $750  for  a  horse  and  carriage ;  if  the  horse  cost 
$120  more  than  the  carriage,  what  was  the  cost  of  each? 

6.  A  grocer  wishes  to  put  351  pounds  of  tea  into  three  sizes 
of  boxes,  using  the  same  number  of  boxes  of  each  kind.     If  the 


40  MODERN    BUSINESS    ARITHMETIC 

sizes  are  respectively  4,  8,  and  15  pounds  each,  how  many  boxes 
will  be  required  ? 

7.  A,  B,  and  C  are  in  partnership.     A's  gain  is  twice  B's, 
and  B's  is  twice  C's.     If  their  total  gain  is  $2464,  how  much  is 
each  one's  gain? 

8.  A  farm  raises  12775  bushels  of  wheat,  averaging  25  bush- 
els to  the  acre  ;  3663  bushels  of  oats,  averaging  37  bushels  to  the 
acre ;  and  4992  bushels  of  corn,    averaging  52   bushels  to  the 
acre.     How  many  acres  are  there  in  the  farm  ? 

9.  If  the  population  of  the  United  States  is  91,020,000,  what 
is  the  average  number  of  in  habitants  represented  by  each  of  the 
444  Congressmen? 

10.  Prindle  &  Co.'s  sales  averaged  $1252  per  week  for  the 
year.     Counting  52  weeks  and  313  days  to  the  year,  what  were 
his  average  daily  sales  ? 


HOME  WORK— No.  5 

1.  Solve  :     (  15341  -5-  29  )  X  (  8430  •*•  1405  )  ==  1587  X  ? 

2.  The  divisor  is  15,  the  quotient  78,  and  the  remainder  4; 
what  is  the  dividend  ? 

3.  My  taxes  for  5  years  were  as  follows  :     $47  the  first  year, 
$54  the  second,  $65  the  third,  $88  the  fourth,  and  $106  the  fifth; 
what  was  my  average  yearly  taxes  ? 

4.  A  and  B  are  together  worth  $15760,  and  A  is  worth  $1240 
more  than  B  ;  what  is  each  man  worth  ? 

5.  I  sold  a  lot  of  wood  for  $423,  thereby  gaining  $2  per  cord  ; 
if  the  wood  cost  me  $329,  how  many  cords  did  I  sell  ? 


Properties  of  Numbers 

108.  An  Integer  is  a  whole  number. 

109.  An  Even  Number  is  a  number  whose  unit  figure  is 
0,  2,  4,  6,  or  8. 

110.  An  Odd  Number  is  a  number  whose  unit  figure  is  1, 
3,  5/7,  or  9. 

111.  A  Prime  Number  is  one  that  is  not  exactly  divisible 
except  by  itself  or  1  ;  as  2,  3,  5,  7,  11,  13,  etc. 

112.  A  Composite  Number  is  divisible  by  some  number 
besides  itself  and  1  ;   as  4,  6,  8,  9,  12,  15,  etc. 

113.  An  Exact  Divisor  of  a  number  is  one  that  will  di- 
vide it  without  a  remainder.     Thus,  7  is  an  exact  divisor  of .  21. 

114.  A  Factor  of  a  Number  is  an  exact  divisor  of  the 
number.     Thus,  3  is  a  factor  of  15. 

115.  A  Common  Factor,  or  Common  Divisor,  of  two  or 
more  numbers  is  a  number  that  will  exactly  divide  all  of  them. 
Thus,  5  is  a  common  factor  of  10,  15,  20,  25,  etc. 

116.  The  Highest  Common  Factor,  or  Greatest  Com- 
mon Divisor,  of  two  or  more  numbers  is  the  greatest  number  that 
will  exactly  divide  all  of  them.     Thus,   15  is  the  highest  com- 
mon factor  of  45,  60,  and  75,  although  both  3  and  5  are  common 
factors. 

117.  To  Factor  a  number  is  to  find  its  factors  or  divisors. 

118.  A  Multiple  of  a  number  is  a  number  that  is  exactly 
divisible  by  that  number.     Thus,  32  is  a  multiple  of  8. 

119.  A  Common  Multiple  of  two  or  more  numbers  is  a 
number  that  is  exactly  divisible  by  each  of  them.     Thus,   84  is 
a  common  multiple  of  of  6  and  7. 

120.  The  Least  Common  Multiple  of  two  or  more  num- 
bers is  the  least  number  that  is  divisible  by  each  of  them.     Thus, 
42  is  the  least  common  multiple  of  6  and  7. 


42  MODERN    BUSINESS    ARITHMETIC 

121.  PRINCIPLES  : 

1.  A  divisor  of  a  number  will  divide  any  multiple  of  that  num- 
ber. 

2.  A  common  divisor  of  two  or  more  numbers  will  divide  their 
sum  and  also  their  difference. 

3.  Every  multiple  is  equal  to  the  product  of  its  prime  factors. 

4.  A  common  multiple  of  two  or  more  numbers  contains  the 
prime  factors  of  those  numbers. 

122.  Cancellation  is  a  process  of  shortening  operations  in 
division  by  rejecting  common  factors  from  both  dividend   and 
divisor. 

123.  Divisibility  of  Numbers  : 

1 .  All  even  numbers  are  divisible  by  2 . 

2.  Any  number  is  divisible  by  3  if  the  sum  of  its  digits  is 
divisible  by  3. 

3.  By  4  if  the  two  right  hand  digits  express  a  number  that  is 
divisible  by  4. 

4.  By  5  if  the  number  ends  in  0  or  5. 

5.  By  6  if  the  number  is  divisible  by  2  and  3. 

6.  By  8  if  the  three  right  hand  digits  express  a  number  divis- 
ible by  8. 

7.  By  9  if  the  sum  of  the  digits  is  divisible  by  9. 

8.  By  10  if  the  number  ends  in  0. 

9.  By  12  if  the  number  is  divisible  by  3  and  4. 

10.  By  15  if  the  number  is  divisible  by  3  and  5. 

11.  By  18  if  the  number  is  divisible  by  2  and  9. 

12.  By  7,  11,  and  13  if  the  number  is  1001  or  any  multiple  of 
it;  as,   20Q2,  5005,  12012,  etc. 

124.  PRINCIPLE  :     A   number   is   divisible   by   any  number 
whose  factors  it  contains. 

125.  To  Find  the  Prime  Factors  of  a  Number. 

Divide  the  number  by  one  of  its  prime  factors,  this  quotient  by 
another,  and  so  on  until  the  last  quotient  is  a  prime  number.  The 
several  divisors  and  the  last  quotient  are  the  prime  factors. 


PROPERTIES    OF    NUMBERS  43 

What  are  the  prime  factors  of  1386  ? 
2)1386 

3)693        The  divisors  2,  3,  3,   7,  and  the  quo- 
3)231     tient  11  are  the  prime  factors. 
7)77 
1  1 
Find  the  prime  factors  of  the  following : 

1.  2445  5.  2366 

2.  2934  6.  1140 

3.  2205  7.  1155 

4.  2310  8.  6300 

126.  To  Find  the  Highest  Common  Factor  of  Two 
or  more  Numbers. 

Take  the  product  of  all  the  common  prime  factors ;  the  result  will 
be  the  highest  common  factor . 

What  is  the  highest  common  factor  of  48,  72,  and  120. 
2)48     72     120 

2)24     36        60         The   product   of    the   prime 

2  )  12     18        30     factors  2   X  2  X  2  X  3  =  24, 

3  )  6        9        15     the  highest  common  factor. 

235 
Find  the  highest  common  factor  of  the  following : 

1.  42  and  112  6.  143  and  1001 

2.  96  and  144  7.  138  and  529 

3.  45,  75,  and  105  8.  165,  255,  and  285 

4.  72,  128,  and  192  9.  420,  630,  and  840 

5.  120,  310,  and  360  10.  462,  1078,  and  1694 

127.  To  Find  the  Greatest  Common  Divisor  when 
the  Numbers  are  not  Readily  Factored. 

Find  the  greatest  common  divisor  of  364  and  925. 


975  ANALYSIS  :     This  operation  is  based  on 

728        principles  1  and  2,  article  121.     A  divisor 


247  °f  364  will  divide  twice  364  or  728,  and  the 
284  G.  C.  D.  of  728  and  975  will  divide  their 
I  %  difference,  247  ;  if  this  G.  C.  D.  will  divide 
247  and  364,  it  will  divide  their  difference, 
117  ;  if  it  will  divide  117,  it  will  divide  twice  117,  or  234;  if  it 
will  divide  234  and  247,  it  will  divide  tJieir  difference,  13  ;  if  the 


44  MODERN    BUSINESS    ARITHMETIC 

G.  C.  D.  will  divide  13,  it  will  divide  9  times  13,  or  117.  Since 
13  is  the  greatest  divisor  of  itself,  it  must  be  the  G.  C.  D.  of  the 
given  numbers. 

Find  the  greatest  common  divisor  of  the  following  : 

1.  632  and  1328  6.  1372  and  1650 

2.  527  and  1207  7.  4082  and  8476 

3.  378  and  648  8.  10907  and  14482 

4.  906  and  2192  9.  4746  and  6667 

5.  1358  and  3738  10.  14256  and  32562 

128.  To  Find  the  I/east  Common  Multiple  of  Two 
or  More  Numbers. 

Take  the  product  of  all  the  prime  factors  of  the  greatest  number, 
and  sue h  prime  factors  of  the  other  numbers  as  are  not  found  in  the 
greatest  number,  and  the  result  will  be  the  L.  C.  M.  of  the  num- 
bers. 

What  is  the  least  common  multiple  of  18,  24,  and  54  ? 

2)  18    24    54  2X3X3X4X3  =  216. 

3)  9    12    27         ANALYSIS:     Reject  the  factors  2,   3,   and  3 
3)  3      4      9     which  are  common  to  two  or  more  of  the  num- 
~j~~        ~~^    bers  ;  the  product  of  these  common  factors  and 
the   factors   not   common  will  give  the  least 
common  multiple  of  the  numbers. 

Find  the  least  common  multiple  of  the  following  : 

1.  27,  36,  and  45  6.       8,  12,  18,  27,  and  36 

2.  32,  42,  and  56  7.  10,  25,  75,  150,  and  2:25 

3.  21,  44,  and  126  8.  18,  24,  36,  48,.  72,  and  96 

4.  30,  42,  66,  and  78  9.  17,  51,  85,  153,  and  187 

5.  24,  32,  72,  and  96  10.  5698  and  9324 


PRACTICAL  PROBLEMS 

129.     Solve  the  following  : 

1.  Find  the  greatest  common  divisor  of  792,  2592,  and  3456. 

2.  Find  the  least  common  multiple  of  32,  44,   132,  and  352. 

3.  What  is  the  greatest  number  that  will  divide  5184  and 
6924? 

4.  What  is  the  least  number  that  can  be  exactly  divided  by 
17,  51,  85,  and  119? 


PROPERTIES    OF    NUMBERS  45 

5.  Johnson's  farm  is  in  the  form  of  a  rectangle,   and  is  2925 
feet  wide  by  3458  feet  long.     What  is  the  length  of  the  longest 
board  that  can  be  used  to  fence  it  without  cutting,   and  how 
many  boards  will  be  required  to  build  a  fence  six  boards  high  ? 

6.  What  is  the  smallest  sum  of  money  that  can  be  paid  for 
shoes  at  $1.75,  $2.50,  or  $3.25  ? 

7.  If  Brown,  White,  and  Green  have  $630,  $1134,  and  $1386 
respectively,  and  agree  to  purchase  horses  at  the  highest  price 
per  head  that  will  allow  each  man  to  invest  all  his  money ;  what 
will  be  the  price  paid  and  how  many  horses  will  each  one  buy  ? 

8.  What  is  the  length  of  the  shortest  rope  that  can  be  cut  into 
14,  28,  or  35  foot  lengths? 

9.  What  is  the  smallest  quantity  of  wine  that  will  fill  casks 
holding  either  44,  48,  or  56  gallons  each? 

10.  Arland  has  three  wine  tanks  that  hold  respectively  2109, 
3363,  and  3819  gallons  each.     He  wishes  to  empty  these  tanks 
into  casks  of  uniform  size,  the  largest  that  will  contain  exactly 
the  contents  of  each  tank.     What  must  be  the  size  of  the  casks, 
and  how  many  will  it  take  ? 


HOME  WORK— No.  6 

1.  What  is  the  least  quantity  of  grain  that  exactly  will  fill 
bins  holding  36,  45,  63,  or  72  bushels  each? 

2.  What  is  the  least  sum  of  money  that  exactly  can  be  spent 
for  horses  at  $140,  cows  at  $91,  or  sheep  at  $7  per  head  ? 

3.  A  commission  merchant  wishes  to  ship  30584  bushels  of 
wheat,  3040  bushels  of  corn,   and  1004  bushels  of  oats.     If  it 
must  all  be  shipped  in  bags  of  equal  size,   what  will  each  bag 
hold,  and  how  many  bags  will  be  required  ? 

4.  A,  B.  and  C  have  respectively  $315,  $567,  and  $693  with 
which  to  purchase  horses.     If  they  pay  the  highest  price  possi- 
ble, and  all  pay  the  same  price,  how  many  horses  will  each  buy? 

5.  \Vhat  is  the  least  sum  of  money  that  can  be  spent  for  tea 
at  72^,  or  54^,  or  45^,  or  36^  per  pound  ? 


46 


MODERN  BUSINESS  ARITHMETIC 


Outline  for  Review 


I.  Addition : 

1.  Definitions. 

2.  Sum. 

3:  Sign  of  Addition. 

4.  Sign  of  Kquality. 

5.  Sign  of  Dollars. 

6.  Reading  Method. 

7.  Proof. 

II.  Subtrac  tion : 

1.  Definitions. 

2.  Minuend. 

3.  Subtrahend. 

4.  Difference. 

5.  Sign  of  Subtraction. 

6.  Parenthesis  and  Bar. 

7.  Principle  and  Proof. 

III.  Multiplication : 

1.  Definitions. 

2.  Multiplicand. 

3.  Multiplier. 

4.  Product. 

*    5.  Sign  of  Multiplication. 

6.  Abstract  and  Concrete 

Numbers. 

7.  Short  Methods. 


IV.  Division. 

1.  Definitions. 

2.  Dividend. 

3.  Divisor. 

4.  Quotient. 

5.  Remainder. 

6.  Sign  of  Division. 

7.  Short  and  Long  Division. 

V.  Properties  of  Num- 
bers : 

1.  Integers. 

2.  Odd  and  Even. 

3.  Prime  and  Composite. 

4.  Divisors  and  Factors. 

5.  Greatest  Common  Divisor 

and   Highest   Common 
Factor. 

6.  Multiples. 

7.  Common  and  Least   Com- 

mon Multiple. 

8.  Divisibility  of  Numbers. 

9.  To  Find  the  Highest  Com- 

mon Factor  or  Greatest 
Common  Divisor. 
10.  To  Find  the  Least  Common 
Multiple. 


CANCELLATION 

130.     Cancellation  is  the  shortening  of  operations  in  divis- 
ion by  rejecting  common  factors  from  both  dividend  and  divisor. 

EXAMPLE  :     Divide  12   X  15  X  32  X  40  by  8  X  5  X  9  X  2. 

43  % 

It  X  *3   X  32   X  40       =  32 

*  X    $    X    0    X   20 

*  3 

SOLUTION  :     Reject  the  factors  20,   5,   3,   3,  4,   and  2  in  the 
order  named  ;  the  quotient  will  be  32. 

Solve  the  following : 

1.  9  X  14  X  34  -s-  18  X  17 

2.  28  X  45  X  11  -^  22  X  36 

3.  63  X  25  X  18  -f-  12  X  45 

4.  54  X  36  X  49  -s-  7  X  "9  X    12 

5.  81  X  96  X  64  •*-  128  X  54 

6.  144  X  84  X  16  -*-  1728  X  28 

7.  85  X  92  X  55  -5-  44  X  34  X  46 

8.  1050  X  312  -f-  35  X  10  X  52 

9.  4096  X  1024  H-  256  X  512 

10.     5280  X  12  -*-  3  X  33  X  40  X  8 


PRACTICAL  PROBLEMS 
131.     Solve  the  following  : 

1.  •  How  many  tons  of  hay  at  $18  per  ton  must  be  given   for 
33  cords  of  wood  at  $6  per  cord  ? 

2.  How  many  barrels  of  flour  at  $4  per  barrel  will  pay  for 
256  bushels  of  wheat  at  $1  per  bushel  ? 

3.  How  many  crates  of  eggs,  each  containing  54  dozen,  worth 
25  cents  per  dozen,  will  pay  for  9  barrels  of  sugar,   each  barrel 
containing  325  pounds,  worth  6  cents  per  pound  ? 

4.  A  man  worked  17  days  for  119  bushels  of  barley  worth  40 
cents  per  bushel.     What  was  his' work  worth  per  day? 


48  MODERN    BUSINESS    ARITHMETIC 

5.  How  many  bushels  of  wheat  at  60  cents  per  bushel  will  pay 
for  12  tons  of  coal  at  $7.20  per  ton  ? 

6.  Brown  exchanged  320  bushels  of  corn  worth  75  cents  per 
bushel  for  barley  worth  90  cents,    and   oats  worth  60  cents,    of 
each  an  equal  amount.     How  many  bushels  of  each  did  he  re- 
ceive ? 

7.  How  many  chests  of  tea,  each  containing  72  pounds  worth 
35  cents  per  pound,  will  pay  for  70  boxes  of  prunes,   each  box 
containing  42  pounds  worth  6  cents  per  pound  ? 

8.  L.  W.  Scarlett  bought  two  kinds  of  cloth,  one  kind  at  70 
cents  per  yard,  the  other   at  95  cents  per  yard.     If  he  took  twice 
as  many  yards  of  the  first  as  of  the  second  and  paid  for  both 
with  329  pounds  of  butter  at  35  cents  per  pound,    how  many 
yards  of  each  kind  did  he  buy  ? 

9.  J.  S.  Taylor  exchanged  470  bushels  of  corn  worth  60  cents 
per  bushel,  and  300  bushels  of  barley  worth  70  cents  per  bushel 
for  tea  at  50  cents  per  pound,  coffee  at  30  cents  per  pound,   and 
cocoa  at  40  cents  per  pound,   of  each  an  equal  amount.     How 
many  pounds  of  each  did  he  receive  ? 

10.  D.  M.  Cook  gave  12  bales  of  hops,   250  pounds  to  the 
bale  worth  17  cents  per  pound,  for  calico  worth  5  cents  per  yard, 
muslin  worth  10  cents  per  yard,   and  gingham,   worth  15  cents 
per  yard.     If  there  were  twice  as  many  yards  of  muslin  as  of  cal- 
ico, and  twice  as  many  yards  of  gingham  as  of  muslin,   how 
many  yards  of  each  did  he  buy  ? 


HOME  WORK— No.  7 

(  Solution  and  answers  required.) 

1.  Bring  in  an  original  problem  in  the  subjects  of  Addition 
and  Subtraction,  containing  at  least  twenty  different  numbers. 

2.  Bring  in  an  original  problem  in  Multiplication  containing 
ten  different  short  cuts. 

3.  Bring  in  a  model  bill  of  not  less  than  ten  items,  extended, 
and  footed,  in  which  short  methods  are  used. 

4.  Bring  in  an  original  problem  in  which  the  greatest  com- 
mon divisor  is  to  be  found. 

5.  Bring  in  an  original  problem  in  which  the  least  common 
multiple  is  to  be  found. 


FRACTIONS 

132.  Fractions  represent  parts  of  units  or  things. 

133.  A  Simple  Fraction  represents  one  or  more  of  the 
equal  parts  of  a  unit.     As,  one-half  and  two-thirds  are  fractions. 

134.  A  Fractional  Unit   is  one  of  the  equal  parts  into 
which  a  unit  is  divided.     As,  one-third  is  a  fractional  unit. 

135.  The  Denominator  of  a  fraction  is  written  below  the 
line  and  shows  the  number  of  parts  into  which  the  unit  is  divided. 

136.  The  Numerator  of  a  fraction  is  written   above    the 
line  and  shows  the  number  of  parts  taken  or  considered. 

137.  The  Terms  of  a  fraction  are  its  numerator  and  denom- 
inator.    Thus,  f  is  a  fraction.     The  denominator  8  shows  that 
the  unit  is  divided  into  8  parts.     The  numerator  5  indicates  that 
5  parts  are  taken.     The  terms  are  the  5  and  the  8. 

138.  A  Proper  Fraction  is  one  whose  numerator  is  less 
than  its  denominator.     As,  f ,  f,  J,  etc. 

139.  An  Improper  Fraction  is  one  whose  numerator  is 
equal  to  or  greater  than  its  denominator.     As,  y,  f ,  V,  etc. 

140.  A  Simple  Fraction  is  one  having  a  single  number 
for  its  numerator  and  a  single  number  for  its  denominator,   but 
may  be  either  proper  or  improper.     As,  f ,  1,  etc. 

141.  A  Compound  Fraction  is  a  fraction  of  a.  fraction  or 
two  or  more  fractions  to  be  multiplied  together.     As,  f  X  f  X  -j. 

142.  A  Complex  Fraction  is  one  that  has  a  fraction  in 
either  its  numerator  or  in  its  denominator,  or  in  both. 

Thus,  —  -4-  -5-  are  complex  fractions. 
5      f     1 

143.  A  Mixed  Number  is  a  whole  number  and  a  fraction 
united.     As,  4^,  5^1 

144.  The  Value  of  a  fraction  is  the  quotient  of  its  numera- 
tor divided  by  its  denominator.     Thus,  the  value  of  V"  is  5,  of 

1  .-> 


is  31. 


50  MODERN    BUSINESS    ARITHMETIC 

145.  Principles  of  Fractions : 

1.  Multiplying  the  numerator  or  dividing  the  denominator 
multiplies  the  fraction. 

2 .  Dividing  the   numerator  or  multiplying  the  denominator 
divides  the  fraction. 

3.  Multiplying  or  dividing  both  numerator  and  denominator 
by  the  same  number  does  not  change  the  value  of  the  fraction. 

146.  The  Reciprocal  of  a  number  or  of  a  fraction  is  1  di- 
vided by  the  number  or  by  the  fraction.     As,  the  reciprocal  of  5 
is  1  -*-  5  or  i ;  of  f  is  1  -H  f  or  f . 


Reduction  of  Fractions 

147.  Reduction  of  Fractions  is  changing   their    form 
without  altering  their  value. 

148.  To  reduce  a  fraction  to  Higher  Terms  is  to  express 

its  terms  in  greater  numbers.     As,  f  =  A  =  If  • 

149.  To  reduce  a  fraction  to  I^ower  Terms  is  to  express 

its  terms  in  less  numbers.     As,  -ff  =  \%  =  |. 

150.  A  fraction  is  reduced  to  its  lowest  terms  when  its  num- 
erator and  denominator  have  no  common  factors. 

151.  To  reduce  a  fraction  to  its  lowest  terms,   reject  from 
both  numerator  and  denominator  all  common  factors,   or  divide 
both  numerator  and  denominator  by  their  greatest  common  di- 
visor. 

Reduce  to  their  lowest  terms  : 

1.  «  6. 

2.  If  7. 

3.  JA-  8. 

4.  W*  9. 

5.  T¥&  10. 

152.  To  reduce  a  whole  or  mixed  number  to  an  improper 
fraction,  multiply  the  whole  number  by  the  denominator,  and  to 


FRACTIONS  51 

the  product  add  the  numerator  of  the  fraction,  and  write  the  re- 
sult over  the  denominator. 

EXAMPLE  :     Reduce  8|  to  an  improper  fraction. 
(  8  X  5  )  +  2  ==  42.     Answer,"  -4/. 
Reduce  to  improper  fractions  : 

1.  Hi  5.  96r4r  9.  1264f 

2.  17  J-  6.  148-H  10.  3240J-H 

3.  35J  7.  785H  11.  5674rWg 

4.  78|  8.  725f  12.  34216f 

153.  To  reduce  an  improper  fraction  to  a  whole  or  mixed 
number,  divide  the  numerator  by  the  denominator. 

EXAMPLE  :     Reduce  -HP  to  a  whole  number. 

132  -5-  4  =  33. 

Reduce  to  whole  or  mixed  numbers : 

1.  ***  5.     W  9. 

2.  *i*  6.     W  10. 

3.  W  7.    -W-  11. 

4.  -41-  8.     4tA  12. 

154.  To  reduce  fractions  to  a  common  denominator,  find  the 
the  least  common  multiple  of  the   denominators  for  the  least 
common  denominator.     Divide  this  least  common  denominator 
by  the  denominator  of  each  of  the  given  fractions  and  multiply 
its  numerator  by  the  quotient.     The  result  will  be  the  new  num- 
erators. 

EXAMPLE  :     Reduce  |,  i\,  and  yV  to  their  least  common  de- 
nominator. 

4  )  I  A  1 5  4  X  3  X  2  X  3  =  48,  the  least 

2)23     4         common  multiple  of   the  denomi- 
132         nators. 

48  -4-    8  =  6        6X3=- 18 

48  -*-  12  =  4         4  X     5  =  20  ^  Answer,  i?,  i§, 

48  -s-  16  =  3        3  X  17  =  51 


52  MODERN    BUSINESS    ARITHMETIC 

Reduce  the  following  to  their  least  common  denominator  : 

I-  I,  A,  I  6.     4i,  V,   I 

2.  *,  A,  H  7.    A,  7i,  if 

3.  f,  -H,  «  8.    A,  A,  A,  if 

4.  if,  li,  I  9.     6i-,  I,  9A,   17H 

5.  W,  H,  «  10.    iH,  H,  M,  H 


Addition  of  Fractions 

155.  To  Add  Fractions  Having  a  Common  Denom- 
inator. 

Add  their  numerators,  write  this  sum  over  their  common  denom- 
inator, and  find  the  value  of  the  fraction. 

Add  the  following  : 

1.'  •  t  +  I  +  t  '+  1  6.    A  +  if  +  H 

2.  f+  4  +  i  +  *  7.  Tfc  +  Tfe  +  |« 

3.  A  +  A  +  A  +  H  8-  8i  +  i  +  18f 

4.  «  +  ii  +  «  +  !f  9.  27i  +  45f  +  85J 

5.  I!  +  i!  +  If  +  «  10.  12f  +  35J  +  124| 

NOTE  —  Whole  numbers  and  fractions  may  be  added  separately. 

156.  To  Add  Two  Fractions  Having  a   Common 
Numerator. 

Add  the  denominators,  multiply  this  sum  by  the  common  numer- 
ator, and  write  the  result  over  the  product  of  the  denominators. 


Add  the  following  : 

1.  f  +  ?  6.  H  +  -B 

2.  I  +  I  7.  9f  +  17| 

3.  f  +  A  8.  43T5T 

4.  1  +  A  9.  125A  +  94A 

5.  if  +  M  10. 


FRACTIONS  53 

157.  To  Add  Fractions  Having  neither  a  Common 
Numerator  nor  a  Common  Denominator. 

Multiply  each  numerator  by  the  product  of  all  the  denominators 
except  its  own  for  new  numerators,  write  their  sum  over  the  pro- 
duct of  all  the  denominators. 

EXAMPLE  :     Add  \  +  f  +  f 

2  X  4  X  5  =  40     4/~)    I   4r  _i_  40        loo 

3  X  3  X  5  =  45 


4  x  4  X  3  =  48 


60  60 


Add  the  following : 

!.'*+!  6.     i  +  f  +  | 

2.  I  +  I  7.    i  +  f  +  4 

3.  4  +  |  8.      f  +  A  +  U 

4.  A  +  A  9.     t+i+| 

5.  A  +  if  10.    ?  +  A  +  « 

158.  To  Add  Fractions  by  Reducing  Them  to  their 
Least  Common  Denominator. 

Reduce  the  fractions  to  their  least  common  denominator,  add  their 
numerators,  write  the  result  over  the  least  common  denominator, 
and  find  the  value  of  the  fraction. 

NOTE — Add  whole  numbers  and  fractions  separately. 

EXAMPLE  :     Add  5A  +  ?U  +  12H- 

Adding  5  +  7  +  12  =  24,  sum  of  the  whole  numbers. 

A  +  ii  +  «  ==  «  +  44  +  «  ==  W  -  W. 

24  +  1H  =  25H- 
Add  the  following  : 

2.  A  +  W  +  i*  7.     23I  +  47A  +  82H 

3.  H  +  if  +  41-  8. 

5.     iVoV  +  T¥o°«y  +  TVvV       10.     W  +  145A  + 


54  MODERN    BUSINESS    ARITHMETIC 

Subtraction  of  Fractions 

159.  To  Subtract  Fractions  Having  a  Common  De- 
nominator. 

Write  the  difference  of  the  numerators  over  the  common  denomi- 
nator. 

Solve  the  following  : 

i.  A  —  A  =  ?         6.  m—  ^==? 

2.  H—  tt  =  ?  7.  15|  —  7t  =  ? 

3.  *f—  H==?  8.  45«--4lA==? 

4.  **  —  **  =  ?  9.  82A  —  53«  =  ? 

5.  !»  —  «  =  ?  10.  175JI  —  120ft  =  ? 

NOTE  —  If  the  fraction  of  the  subtrahend  is  the  greater,  write  one  less 
than  the  difference  of  the  whole  numbers  for  the  integral  part,  and  the 
complement  of  the  difference  of  the  fractions  for  the  fractional  part. 

Thus  5-J-  —  2f  =  (  5  —  2  )  less  1  =  2,  and  the  complement  of 
*\  —  i»  which  is  f.  Answer,  2f. 

160.  To  Subtract  Fractions   Having    a    Common 
Numerator. 

Multiply  the  difference  of  the  denominators  by  the  common  num- 
erator and  write  the  result  over  the  product  of  the  denominators. 

EXAMPLE  :     |  —  4=  (7  —  4)  X  3  =  9,  the  numerator. 
4  X  7  =  28,  the  denominator. 
Answer,  ^. 

Solve  the  following  : 

1.  i-l==?  6.     fJ-M  =  ? 

2.  *-*  =  ?  7.     «*-«*  =  ? 

3.  !-—*«?  8.     «?-«?=? 

4.  A  —  A  =  ?  9. 

5.  -=?  10. 


161.  To  Subtract  Fractions  Having  neither  a  Com- 
mon Numerator  nor  a  Common  Denominator. 

From  the  product  of  the  first  numerator  times  the  second  denomi- 
nator take  the  product  of  the  second  numerator  times  the  first  de- 
nominator. Write  this  difference  over  the  product  of  the  denomi- 
nators, 


FRACTIONS  55 


3X3  =  9.     4X2  =  8.     9  —  8'=  1,  the  numerator. 
4  X  3  —  12,  the  denominator.     Answer,  iV 


EXAMPLE  :     I  —  f 

3X3  =  9.     4 
4  X  3  =  12,  tl 

Solve  the  following : 


1.  i  —  f  =  ?  6.  |i-«  =  ? 

2.  |-  *  =  ?  7.  «-      f-? 

3.  *  —  A==?  8.  5i  —  2f  =  ? 

4.  A  ---4==?  9.  17&—  14*  =  ? 

5.  if  ~  II  =  ?  10.  48i  —  32|  =  ? 

162.  To  Subtract  Fractions  by  Reducing  Them  to 
a  Least  Common  Denominator. 

Reduce  the  fractions  to  their  least  common  denominator.  Write 
the  difference  of  their  numerators  over  the  least  common  denomina- 
tor. 

Solve  the  following  : 

1.  H-T7<r  =  ?  6.     8£  —  4|  =  ? 

2.  tt  —  **=*  7.     18A--7==? 

3.  H  —  «  =  ?  8. 

4.  «-!!  =  ?  9. 

5.  ill  —  W  =  ?  10.     1354—  107J  =  ? 


PRACTICAI,  PROBI.BMS 

163.     Solve  the  following  : 

1 .  How  many  yards  of  cloth  in  five  bolts  measuring  45i,  38f , 
47i,  44i,  and  41  f  yards  respectively  ? 

2.  A's  land  consists  of  five  fields  as  follows:     184J,   127|, 
224A,  38i7o,  and  97^  acres.     How  much  does  he  own? 

3.  Sold  7  pieces  of  cloth  containing  25J,  34i,  42i,   18|,   37f, 
26|,  and  4lf  yards  respectively.     How  many  yards  in  all? 

4.  The  sum  of  two  numbers  is  28^ ;    their  difference  is  5j. 
What  are  the  numbers  ? 

5.  What  number  added  to  135|  will  make  178T\  ? 


56  MODERN  BUSINESS  ARITHMETIC 

6.  A  merchant  received  a  $20  bill    to    pay    for   flour 
sugar  $2  f,   coffee  $3f,   and  tea  $1-J.     What  change  should  he 
give  ? 

7.  Bought  goods  for  $1251,   $82fc,   $87f,   and  sold  them  for 
$425^-,  how  much  was  the  profit? 

8.  My  first  year's  gain  was  $874|,   the  second  was  $1135$, 
my  third  was  as  much  as  the  first  and  second,  my  fourth  was   a 
loss  of  $235|.     What  was  my  total  gain  for  the  four  years? 

9.  My  income  for  the  first  month  was  $55i  and  for  each  of 
the  succeeding  eleven  months  was  increased  $5J.     What  was 
my  total  income  for  the  12  months  ? 

10.  A's  share  in  a  business  was  $2345},  B's  was  $425|  more, 
C's-was  $1271i  less  than  A's  and  B's  together.     What  was  B's 
and  C's  capital  and  what  was  the  total  investment  ? 

11.  A  man  made  purchases  of  $!•}-,  $2f,  $3|,  and  $7f.     What 
change  should  he  receive  from  a  $20  gold  piece  ? 

12.  A  merchant  bought  48  bbls:  of  flour  at  $5j  per  bbl.   and 
sold  it  for  $6f  per  bbl.     What  was  his  profit? 

13.  I  bought  a  quantity  of  coal  for  $155  &,  and  of  lumber  for 
$345|.     I  sold  the  coal  for  $173i,    and   the  lumber  for  $390}. 
What  was  my  gain  ? 

14.  January's  sales  were  $5840f .     If  each  of  the  subsequent 
monthly  sales  were  increased  by  $1235},  what  were  the  entire 
sales  for  the  year  ? 

15.  A  merchant's  sales  for  Monday  were  $72$,   for  Tuesday 
they  increased  $15],  for  Wednesday  $25f ,   for  Thursday  $18  j80-^ 
for  Friday,  $5|,   and  for  Saturday  $44  J.     What  was  the  total 
sales  for  the  week  ? 


FRACTIONS  57 

Multiplication  of  Fractions 

164.  To  Multiply  a  Fraction  by  a  Whole  Number. 

Multiply  the  numerator  by  the  whole  member  and  divide  the  pro- 
duct by  the  denominator. 

Solve  the  following : 

1.  7  X  f  =  ?  6.  125  X  |  =  ? 

2.  9  X  4  ==  ?  7.  482  X  £  =  ? 

3.  16  X  A  =  ?  8.  666  X  A  =  ? 

4.  48  X  f  =  ?  9.  597  X  \\ -  =  ? 

5.  150  X  | -  =  ?  10.  885  X  J|  =  ? 

165.  To  Multiply  a  Fraction  by  a  Fraction. 

Multiply  the  numerators  together  for  a  new  numerator,  and  the 
denominators  together  for  a  new  denominator.     Cancel  if  possible. 

Solve  the  following : 

1.  t  X  f  X  U  =  ?    .  6.  H  X  2§  =  ? 

2.  |  X  T70  X  A  =  ?  7.  3|  X  54  —  ? 

3.  4  X  |  X  |  X  £  =  ?  8.  7t  X  2f  X  4i  =  ? 

4.  f  X  «  X  if  X  A  =  ?  9.  12i  X  74  X  | -  =  ? 

5.  «  X  if  X  «  X  -B  =  ?  10.  18f  X  241  X  TV  =  ? 

166.  To  Find  the  Product  of  Two  Mixed  Numbers 
whose  Integers  are  Identical  and  the  Sum  of  whose 
Fractions  is  a  Unit. 

To  the  product  of  the  integer  times  one  greater  annex  the  product 
of  the  fractions . 

EXAMPLE  :     Multiply  4i  by  4f . 

4  X  5  =  20.     i  X  f  =  A.     Answer,  20 A- 

Solve  the  following : 

1.  2i  X  2f  =  ?  6.  15|  X  15J  =  ? 

2.  54  X  5t  =  ?  7.  24T\  X  24A  ==  ? 
'3.     6£X6f  =  ?  8.  58tX58i  =  ? 

4.  8f  X  8f  =  ?  9.  74i  X  74}  =  ? 

5.  12J-  X  12J-  =a  ?  10.  89|  X          == 


58  MODERN    BUSINESS    ARITHMETIC 

167.  To  Find  the  Product  of  any  Two  Mixed  Num- 
bers whose  Fractions  are  %. 

To  the  product  of  the  integers  add  one-half  their  sum  and  an- 
nex \. 

EXAMPLE  :     24  X  44  =  2X4+3+i=  \\\. 
34X44  =  3X4  +  34  +  1  =  15}. 
Solve  the  following : 

1.  Multiply  24  by  64  6.     Multiply  94  by  111 

2.  Multiply  34  by  54  7.     Multiply  154  by  174 

3.  Multiply  34  by  71  8.     Multiply  454  by  614 

4.  Multiply  44  by  54  9.     Multiply  884  by  1024 

5.  Multiply  84  by  124  10.     Multiply  944  by  1164 

168.  To  Find  the  Product  of  Two  Numbers  whose 
Integers  are  Identical. 

To  the  product  of  the  integers  add  the  product  of  the  sum  of  the 
fractions  times  the  common  integer  and  the  product  of  the  fractions . 

EXAMPLE  :     64  X  6J  =  (6  X  6  +  (6  X  f )  +  (4  X  |), 

or  36  +  5  +  i  =  4H. 
Solve  the  following : 

1.  Multiply  84  by  8i  6.  Multiply  45f  by  45 } 

2.  Multiply  12i  by  12|  7.  Multiply  48}  by  48f 

3.  Multiply  14f  by  14$          8.  Multiply  60£  by  60| 

4.  Multiply  24f  by  24f  9.  Multiply  81|  by  81| 

5.  Multiply  35i  by  35|         10.  Multiply  120}  by  120& 

169.  To  Find  the  Product  of  Two  Mixed  Numbers 
when  the  Fractions  are  Identical. 

To  the  product  of  the  integers  add  the  product  of  the  sum  of  the 
integers  times  the  common  fraction  and  the  product  of  the  fractions . 

EXAMPLE:     4J  X  8*  =  (4  X  8)  +  (12  X  4  +  (i  X  t), 

or  32  +  4  +  i  =  36i 
Solve  the  following : 

1.  Multiply  6J  by  18J  6.     Multiply  27f  by  21| 

2.  Multiply  9i  by  15i  7.     Multiply  55f  by  22f 

3.  Multiply  36i  by  44J  8.     Multiply  88|  by  llf 

4.  Multiply  72f  by  36|  9 .     Multiply  1 1 7f  by  51  ? 

5.  Multiply  47f  by  53}  10.     Multiply  234T7T  by  481A 


FRACTION  vS  59 

Division  of  Fractions 

170.  To  Divide  a  Fraction  by  a  Whole  Number. 

Divide  the  numerator  or  multiply  the  denominator  by  the  whole 
number. 

EXAMPLE  :     I  -*-  2  =  f,  by  dividing  numerator. 

%  -r-  2  =  VV  ~  f  >  by  multiplying  denominator. 

Solve  the  following : 

1.  Divide  A  by  4  6.  Divide  4f  by  8 

2.  Divide!  if  by  6  7.  Divide  12$  by  9 

3.  Divide  }f  by  7  8.  Divide  32}  by  49 

4.  Divide  ft  by  9  9.  Divide  48  f  by  64 

5.  Divide  ft  by  18  10.  Divide  54^  by  119 

171.  To  Divide  a  Whole  Number  by  a  Fraction. 

Multiply  the  whole  number  by  the  denominator  and  divide  the  re- 
sult by  the  numerator  of  the  fraction. 

EXAMPLE  :     8  -*-  f .     8  X  3  =  24.     24  ^  2  =  12. 
Solve  the  following : 

1.  Divide  9  by  I  6.  Divide  65  by  f 

2.  Divide  15  by  |  7.  Divide  78  by  if 

3.  Divide  28  by  |  8.  Divide  96  by  if 

4.  Divide  42  by  }f  9.  Divide  144  by  \\ 

5.  Divide  57  by  if  10.  Divide  272  by  \\ 

172.  To  Divide  a  Fraction  by  a  Fraction. 

Reduce  whole  or  mixed  numbers  to  improper  fractions.  Invert 
the  divisor  and  proceed  as  in  multiplication  of  fractions.  Cancel  if 
possible. 

EXAMPLE  :     Divide  f  X  f  by  3J  X  4. 

|  X  f  X  A  X  i  =  |  Ans. 
Solve  the  following : 

1.  *  X  *  -*-  iV  X  A  6.  41  X  1\  -+-  3T34  X  2i 

2.  |  -X  A  X  |  H-  I  X  if  7.  21  -f-  i  X  |  X  |  X  | 

3.  f  X  ii  -*•  If  X  |  X  |  8.  f  X  *  X  f  X  f  •*-  If 

4.  *  X  «  X  if  -s-  ii  X  if  9.  5f  -*-  5i  X  5J 

5-  «  X  if  -s-  |  X  A  X  A  10.  7i  X  9J  -f-  1 J  X  6A 


60  MODERN    BUSINESS    ARITHMETIC 

173.     To  Reduce  Complex  Fractions. 

Divide  the  numerator  of  the  complex  fraction  by  the  denomina- 
tor as  in  division  of  fractions. 

EXAMPLE  :     Reduce  fi  =  3£  -5-  7i  =  t  X  A  =  ff  . 

7i 
Reduce  the  following  : 

15? 

2       251 
4A 

7 

5 


6. 

_2  !  3_ 

1*  X  3i 

4i  4-  3* 

' 

7i-  +  5A 

8. 

156} 

2i  ji 

9. 

il 

7 

1  n 

*  +  (f  X  3iO--(2rx  H) 

J.U. 

2i2oV  +  2f 

X  i?   X  7i 

PRACTICAL, 

174.     Solve  the  following  : 

1.  A  man  gave  %  of  his  fortune  to  his  son,  YZ  to  his  daughter, 
and  the  remainder,  $3500,  to  his  wife.     How  much  did  his  son 
and  daughter  each  receive  ? 

2.  A  man  owned  YI  of  a  business,   and  then  bought  %  as 
much  more.     He  then  sold  %  of  his  interests  for  $1200.     What 
was  the  value  of  the  whole  business  ? 

3.  A's  income  is  $2500  per  year.     If  he  spends  \  of  f  of  it 
for  board,  f  of  f  of  the  remainder  for  clothes,  |  of  fV  of  the  re- 
mainder for  books,  and  saves  f  of  the  remainder,  how  much  can 
he  save  in  three  years  ? 

4.  A  man  at  his  death  left  his  wife  $12500,  which  was  \  of  | 
of  his  estate.     At  her  death  she  left  f  of  her  share  to  her  daugh- 
ter.    What  part  of  her  father's  estate  did  the  daughter  receive 
from  her  mother  ? 

5.  Jones's  investment  is  4  of  Brown's,  and  Brown's  is  •§•  of 
Green's.     If  their  total  investment  is  $4830,  what  is  each  one's 
share  ? 

6.  Brown  lost  ^  of  his  investment  the  first  year.     The  sec- 
ond year  he  gained  $400,   and  then  had  $800.     What  was  his 
original  investment? 


FRACTIONS  61 

7.  Smith  bought  a  stock  of  goods  and  sold  }i  of  it  at  a  gain 
of  $300,  y*  at  a  gain  of  $500,   and  the  remainder  at  a  loss  of 
$200.     What  was  the  first  cost  of  the  goods,  if  the  net  gain  was 
l/6  of  the  cost  ? 

8.  Muir,  Nunn,  and  Hakes  receive  $920  for  doing  a  job  of 
work.     How  much  should  each  one  get  if  the  money  is  divided 
in  proportion  to  % ,  ^ ,  and  ^ . 

9.  Bought  27 %  yards  of  matting  at  23 X  cents  a  yard,   and 
paid  for  the  same  in  eggs  at  13 K  cents  a  dozen.     How  many 
dozen  eggs  were  required  ? 

10.  A  merchant  invested  %  of  his  money  in  shoes,  }i  —  $100 
in  groceries,  ^  +  $200  in  tea  and  coffee,  Y%  +  $250  in  hay  and 
grain,  and  deposited  the  remainder,  $588,  in  the  bank.  What 
was  the  total  value  of  his  property,  and  how  much  did  he  invest 
in  each  kind  of  stock  ? 


HOME  WORK-NO.  8 

1.  The  sum  of  two  numbers  is  12%  ;  their  difference  is  3%. 
What  are  the  numbers  ? 

2.  A  can  do  a  piece  of  work  in  4/^  days.     If  it  takes  B  twice 
as  long  as  A,  and  C  ft  as  long  as  B,  how  long  will  it  take  C  to 
do  it? 

3.  A  and  B  together  have  $1190.     If  Y\  of  A's  equals  ^   of 
B's,  how  much  has  each  ? 

4.  A  120  gallon  tank  has  a  pipe  that  will  flow  15  gallons  in 
12  minutes.     If  another  tank  holding  180  gallons  has  a  pipe  that 
flows  20  gallons  in  10  minutes,  which  tank  will  empty  first,   and 
in  how  much  less  time  ? 

5.  Blank  saves  ^  of  YZ  of  his  income,  and  Black,  having  the 
same  income,  spends  2>^  times  as  much  as  Blank,   and  at  the 
end  of  the  year  finds  himself  $150  in  debt.     What  is  the  income 
of  each  ? 

6.  Willis  sold  goods  for  $2340  and  gained  ys  of  the  cost.     If 
he  had  sold  them  for  $2050,  would  he  have  gained  or  lost,   and 
how  much  ? 


62  MODERN    BUSINESS    ARITHMETIC 

7.  Brown  bought  a  house  and  lot  paying  %   the  price  down, 
and  the  second  payment  was  X  the  remainder  due.     If  the  sum 
of  the  two  payments  thus  made  was  $2100,   what  was  the  cost 
price  of  the  place  ? 

8.  A  boy  lost  YZ  of  ^  of  his  kite  string,  then  added  60  feet. 
He  then  lost  /^  of  what  he  then  had,   then  by  adding  60  feet 
found  it  Y^  of  its  original  length.     What  was  its  length  at  first? 

9.  A  pole  is  y?  in  the  mud,  X  in  the  water,  and  the  part  in 
the  air  is  >i  its  length  plus  23  feet.     What  is  the  length  of  the 
pole? 

10.  A's  automobile  travels  21  miles  in  45  minutes,  and  B's 
will  travel  30  miles  in  65  minutes.  If  the  race  course  is  195 
miles  long,  which  will  win,  and  by  how  much  time? 


DECIMALS 


175.  A  Decimal  Fraction  is  a  fraction  whose  denomina- 
tor is  10,  100,  1000,  etc.     Thus,  T\,  -ffo,  TVoV  are  decimal  frac- 
tions. 

176.  A  Decimal  has  the  same  value  as  a  decimal  frac- 
tion, and  is  expressed  by  writing  the  numerator  only,   the  de- 
nominator being  indicated  by  the  number   of  decimal   places. 
Thus,    .3,    .27,    .125,   are  decimals  and  are  read  three- tenths, 
twenty-seven  hundred ths,  etc. 

177.  The  Decimal  Sign  (  .  ),  called  the  decimal  point,   is 
used  to  separate  the  decimal  from  the  units  place. 

178.  A   decimal  always  contains  as  many  decimal  places  as 
there  are  ciphers  iu  the  denominator  of  an  equivalent  decimal  frac- 
tion. 

179.  A  Pure  Decimal  consists  of  a  decimal  only.     Thus, 

.5,  .25,  .375. 

180.  A  Mixed  Decimal  consists  of  a  whole  number  and  a 
decimal.     Thus,  4.5,  6.25,  27.375. 

181.  Decimals  increase  from  right  to  left  and  decrease  from 
left  to  right  in  a  ten  fold  ratio,  the  same  as  whole  numbers. 

182.  Decimals  are  read  the  same  as  d'ecimal  fractions.     Thus, 
.8  is  read  eighth- tenths,  and  .75  is  read  seventy-five  hundredths. 

183.  Read  the  following  : 

1.  .9  6.  .04 

2.  .34  7.  .2045 

3.  .345  8.  .00705 

4.  .2487  9.  234.010735 

5.  .35362  10.  2004.4002 

184.  Write  the  following  : 

1.  Eleven  hundredths. 

2.  Forty- two  thousandths. 

3.  Seven  hundred  five  ten  thousandths. 


64  MODERN    BUSINESS    ARITHMETIC 

4.  Five  thousand  two  hundred  ten  hundred  thousandths. 

5.  Two  hundred  five  thousand  six  hundred  four  millionths. 

6.  Twenty-seven  and  two- tenths. 

7.  One  hundred  ten  and  thirty-five  thousandths. 

8.  Thirty-three  and  one-third,  hundred ths. 

9.  Three  thousand  and  three  thousandths. 

10.  Seventy-two  million  and  seventy-two  millionths. 


Reduction  of  Decimals 

185.  To  Reduce  a  Decimal  to  a  Common  Fraction. 

Write  for  the  denominator  I  with  as  many  ciphers  as  there  are 
decimal  places  in  the  decimal  and  reduce  the  resultant  fraction  to 
its  lowest  terms. 

Reduce  to  common  fractions  : 

1.  .8  6.  .121 

2.  .75  7.  .37} 

3.  .625  8.  4.125 

4.  .1525  9.  18.41875 

5.  .4875  10.  145.33J 

186.  To  Reduce  a  Common  Fraction  to  a  Decimal. 

Annex  ciphers  to  the  numerator  and  divide  by  the  denominator. 
Point  off  as  many  decimal  places  as  ciphers  used. 

Reduce  to  decimals : 

1.  \  6.  5i 

2.  |  7.  27i 

3.  1  8.  64| 

4.  A  9.  4.2A 

5.  H  10-    87  A 


Addition  of  Decimals 

187.     To  Add  Decimals. 

Reduce  all  fractions  to  decimals.  Write  units  of  like  order  in 
the  same  columns.  Add  as  in  whole  numbers,  placing  the  decimal 
point  between  the  units'  and  tenths^  places. 


FRACTIONS  65 

Find  the  sum  of  the  following : 

1.  .245,  .76,  .358,  .1976,  .40257,  .38964 

2.  .25.2,  1.8,  325.4,  60.02,  7.6025 

3.  425.,  .785,  30.972,  .046,  .0002,  880 

4.  i,   f,   T36,   I,   TV 

5.  2t,  27i,  6.2i,  387.5,  .3125,  8f 


Subtraction  of  Decimals 

188.     To  Subtract  Decimals. 

Reduce  all  fractions  to  decimals.  Write  units  of  like  order  in 
same  columns.  Subtract  as  in  whole  numbers,  placing  the  decimal 
between  units1  and  tenths1  places. 

Solve  the  following : 

1.  From  42.5  take  35.3  6.  From  f  take  .54 

2.  From  212.25  take  93.5  7.  From  8.02  take  8.002 

3.  From  1216J  take  93.5  8.  From  126.5  take  12.65 

4.  From  ?i  take  3A  9.  From  47i  take  2.5i 

5.  From  1.275  take  .031  10.  From  7896  take  69.87 


Multiplication  of  Decimals 

189.     To  Multiply  Decimals. 

Multiply  as  in  whole  numbers.  From  the  right  point  off  as 
many  decimal  places  in  the  product  as  there  are  in  both  multiplier 
and  multiplicand. 

Solve  the  following : 

1.  Multiply  .75  by  .5  6.  Multiply  4^  by  7.5 

2.  Multiply  1.25  by  .25  7.  Multiply  .375  by  6J 

3.  Multiply  41.75  by  .03  8.  Multiply  23.54  by  41.5 

4.  Multiply  2.1875  by  1.5  9.  Multiply  7^  by  6i 

5.  Multiply  .0525  by  .0035  10.  Multiply  1.5}  by  93J. 


66  MODERN    BUSINESS    ARITHMETIC 

Division  of  Decimals 

190.     To  Divide  Decimals. 

If  necessary ,  annex  ciphers  to  the  dividend  and  divide  as  in  whole 
numbers.  From  the  right,  point  off  as  many  decimal  places  in  the 
quotient  as  those  in  the  dividend  exceed  those  in  the  divisor. 

Solve  the  following : 

1.  Divide  2.16  by  3.6  6.  Divide  \1\  by  .35 

2.  Divide  9.654  by  .03  7.  Divide  8^  by  .625 

3.  Divide  102.4  by  .32  8.  Divide  .00261  by  300 

4.  Divide  1850  by  .25  10.  Divide  202.002  by  .006 


Circulating  Decimals 

191.  A  Circulating  Decimal  is  a  decimal  in  which  a  fig- 
ure  or   set   of   figures    are   repeated  indefinitely.     Thus,   ^   — 
.3333  +  ,  and  A  =  .727272  +  . 

192.  A  Repetend  is  the  repeated  figure  or  figures,   and  is 
represented  by  a  dot  over  the  repeated  part.     Thus,    .3333  + 

.3,  .727272+  =  -  .72,  and  .135135135+  :  -  .135. 

193.  A  repetend  arises  from  the  reduction  of  a  common  frac- 
tion whose  denominator  is  not  a  factor  of  10,  100,  1000,  etc. 

194.  A  repetend  may  be  reduced  to  a  common  fraction  by 
using  for  its  denominator  as  many  9's  as  there  figures  in  the  re- 
petend.    Thus,  .3  ==  |  ==  i  .72  ==  -5 §  ==  -A,  .135  ==  iSi  =  iV\ 
—  35T- 

195.  To  add  or  subtract  repetends,  continue  repetend  of  each 
number  until  they  terminate  at  the  same  place.    Add  or  subtract 
as  in  finite  decimals,  carrying  when  necessary.     Thus, 

.333333 

.727272 
.135135 


1.195741 

196.  In  multiplication  and  division  of  decimals,  it  is  best  to 
reduce  repetends  to  common  fractions  and  then  multiply  or  di- 
vide as  required. 


DECIMALS  67 

197.     Solve  the  following  : 

1.  Reduce  f  to  a  circulating  decimal. 

2.  Reduce  f  to  a  circulating  decimal. 

3.  Reduce  ^  to  a  circulating  decimal. 

4.  Reduce  .45  to  a  common  fraction. 

5.  Reduce  .513  to  a  common  fraction. 

6.  Reduce  .142857  to  a  common  fraction. 

7.  Add  .35  +  .7  +  .137  +  .18  +  .241.* 

8.  Add  i\  +  .230769  and  reduce  to  a  common  fraction. 

9.  From  f  take  .432  and  reduce  to  a  repetend. 

10.  From  .758241  take  .571428  and  reduce  to  a  common  frac- 
tion. 


PRACTICAL  PROBLEMS 

198.     Solve  the  following  : 

1.  How  many  acres  in  a  farm  consisting  of  five  fields  as  fol- 
lows :     55/4  acres  of  wheat,  72.75  acres  of  corn,   27^   acres  of 
oats,  18^  acres  of  barley,  and  21.625  acres  of  pasture  land? 

2.  How  many  chains  in  length  will  be  the  total  distance 
around  three  fields,   each  77.15  chains  long  and  54.375  chains 
wide? 

3.  A's  ranch  consisted  of  1274.3   acres,    and   B's  of  935.25 
acres.     How  much  more  land  did  A  own  than  B  ? 

4.  Find  the  difference  between  $932 X  and  $9.32^. 

5.  A  man  who  owned  2460|  acres  of  land,  sold  375|  acres  to 
A,  1050.25  acres  to  B,  and  428.1875  to  C.     How  many  acres  re- 
mained unsold  ? 

6.  If  a  cord  of  wood  is  worth  $5.75,  what  are  12.25  cords 
worth  ? 

7.  If  wheat  is  worth  $.87/4   per  bushel,   how  many  bushels 
can  be  bought  for  $93.625  ? 


68 


MODERN    BUSINESS    ARITHMETIC 


8.  How  many  bushels  of  oats  at  $.16/i   per  bushel   can  be 
bought  for  $51.50? 

9.  An  automobile  travels  at  the  rate  of  27 1  miles  per  hour. 
How  far  will  it  travel  in  12^  hours  ? 

10.  A  man  sold  a  horse  for  $125,  and  received  in  payment 
12  }4  yards  of  cloth  worth  $3/^  per  yard,  and  the  remainder 
in  tea  at  $.62)4  per  pound.  How  many  pounds  of  tea  were  re- 
quired ? 


Outline  for  Review 


I.  Common  Fractions : 

1.  Definition. 

2.  Fractional  unit. 

3.  Terms: 

Denominator. 
Numerator. 

4.  Kinds : 

Proper. 

Improper. 

Simple. 

Compound. 

Complex. 

Mixed  number. 

5.  Value  of  a  fraction. 

6.  Principles  of  fractions. 

II.  Decimals : 

1.  Definition. 

2.  A  decimal. 

3.  The  decimal  sign. 

4.  Kinds  of  decimals: 

Pure  decimal. 
Mixed  decimal. 

5.  Reduction  of  decimals. 


7 .  Reduction  of  fractions  : 

To  higher  terms. 

To  lower  terms. 

To  an  improper  fraction. 

To  whole  or  mixed  numbers. 

To  a  common  denominator. 

8.  Addition  of  fractions. 

9.  Subtraction  of  fractions. 

10.  Multiplication  of  fractions. 

11.  Division  of  fractions. 

12.  To    reduce    complex   frac- 

tions to  simple. 


6.  Addition  of  decimals. 

7.  Subtraction  of  decimals. 

8.  Multiplication  of  decimals. 

9.  Division  of  decimals. 
10.  Circulating  decimals. 


Decimal  Currency 

199.  Money  is  any  stamped  metal  or  other  substance  legally 
used  as  a  medium  of  commerce. 

200.  Currency  is  the  money  of  a  country. 

201.  Coin  is  stamped  metal  used  as  currency. 

202.  A  Decimal  Currency  is  a  currency  based  upon  the 
decimal  system  of  notation. 

203.  The  United  States,  Canada,  France,  and  Germany  have 
each  adopted  a  more  or  less  imperfect  decimal  system. 


United  States  Money 

204.  United  States  Money  is  the  legal  currency  of  this 
country.     The    system    was   adopted   in    1786,    and   has   been 
changed  several  times  by  acts  of  congress. 

205.  The  Coins  of  the  United  States  are  made  of  gold,   sil- 
ver,   nickel-copper,    and    bronze.     Gold  and  silver  are   mixed 
with  a  base  metal,  called  alloy, — nine  parts  pure  metal  and  one 
part  alloy. 

206.  The  Gold  Coins  of  the  United  States  are  : 
The  Double  Eagle,  value  $20,  weight  516  grains. 
The  Eagle,  value  $10,  weight  258  grains. 

The  Half  Eagle,  value  $5,  weight  129  grains. 

NOTE — The  THREE  DOLLAR  piece,  the  QUARTER  EAGLE,  and  the  ONE 
DOLLAR  piece  are  no  longer  coined.  The  weight  of  the  $1  piece  is 
25.8  grains. 

207.  The  Silver  Coins  of  the  United  States  are  : 
The  Standard  Dollar,  value  $1,  weight  412.5  grains. 
The  Half  Dollar,  value  50^,  weight  192.9  grains. 
The  Quarter  Dollar,  value  250,  weight  96.45  grains. 
The  Dime,  value  10^,  weight  38.58  grains. 


70  MODERN    BUSINESS    ARITHMETIC 

208.  The  Nickel- Copper  Coin  of  the  United  States  is  the 
Five  Cent  piece,  value  5^,  weight  77.16  grains. 

NOTE — The  FIVE  CENT  piece  (silver)  and-  the  THREE  CENT  piece 
(  nickel-copper  )  are  no  longer  coined.  The  NICKEL  is  composed  of  25 
parts  nickel  and  75  parts  copper. 

209.  The  Bronze  Coin  of  the  United  States  is  the  One  Cent 
piece,  value  1^,  weight  48  grains. 

NOTE — The  ONE  CENT  piece  is  composed  of  95  parts  copper  and  5 
parts  alloy. 

210.  Money  is  called  a  Legal  Tender  when  the  law  re- 
quires that  it  be  received  in  payment  of  a  debt. 

211.  United  States   Gold  Coins   of   standard  weight    are 
legal  tender  for  all  debts  in  the  United  States. 

212.  Standard  Silver  Dollars  are  legal  tender  for  all 
debts  not  under  special  contract  to  the  contrary.     The  other 
silver  coins  are  legal  tender  in  sums  not  exceeding  ten  dollars. 

213.  The  Nickel  and  One  Cent  piece  are  legal  tender  in 
sums  not  exceeding  twenty-five  cents. 

214.  The  Paper  Money  of  the  United  States  consists  of 
Treasury  Notes  (  Greenbacks  ),    Gold  Certificates,   Silver  Certifi- 
cates, and  National  Bank  Notes. 

215.  Greenbacks,  or  treasury  notes,  are  issued  by  the  gov- 
ernment, and  are  legal  tender  for  all  debts  except  duties  on  im- 
ports and  interest  on  government  bonds  payable  in  gold. 

216.  Gold  Certificates  and  Silver  Certificates  are  is- 
sued by  the  government  to  represent  coin  in  the  treasury.    They 
are  principally  used  to  facilitate  the  handling  of  large  amounts 
of  cash. 

217.  National  Bank  Notes  are  furnished  by  the  govern- 
ment   and   issued   by    National   Banks    which  are   required  to 
deposit  an  equal  amount  of  U.  S.  bonds  with  the  government  as 
security  for  their  redemption.     They  are  not  legal  tender   but 
on  account  of  the  security  given,  circulate  without  question. 


DECIMAL  CURRENCY  71 

218.  Table  for  United  States  Money: 

10  mills      =  1  cent ^,  or  ct. 

10  cents     —  1  dime d. 

10  dimes    =  1  dollar.... $. 
10  dollars  =  1  Eagle.... E. 

219.  The  Unit  of  measure  is  the  dollar,  and  sums  of  money 
are  spoken  of  as  dollars  and  cents.     The  Eagle  and  dime  are  sel- 
dom mentioned  in  business  transactions. 

220.  To  reduce  United  States  money  to  higher  denomina- 
tions, move  the  decimal  point  to  the  left ;  to  lower  denomina- 
tions, move  the  decimal  point  to  the  right.     Thus  : 

$80.  =  8.  Eagles;  $35.  =  350.  dimes;  $25.  =  2500.  cents. 


Addition  and  Subtraction 

221.  To  Add  or  to  Subtract  United  States  money. 

Write  units  of  like  denomination  in  same  columns.     Add  or 
subtract  as  in  simple  numbers. 

222.  Solve  the  following  : 

1.  Add  35  dollars,  148  dollars  and  twenty-five  cents,  7  dollars 
and  seventeen  cents,  and  one  hundred  dollars  and  52  cents. 

2.  From  eight  hundred  forty  dollars  and  five  cents,  subtract 
three  hundred  four  dollars  and  thirty  cents. 

3.  Monday's  sales  were  $517. 62;  Tuesday's,  $478.25  ;  Wed- 
nesday's,   $524.88;    Thursday's,    $495.35;    Friday's,    $392.07; 
Saturday's,  $812.22.     Find  the  total  sales  for  the  week. 

4.  Jones's  checks  for  the  month  of  January  were  as  follows  : 

$28.75,  $32.80,   $105.40,   $75.25,   $1250,   $35.95,  $67.20.     Find 
the  total  amount  withdrawn. 

5.  Brown  deposited  the  following  sums  to  his  credit :     $750, 
$250,  $325.50,   $18.40,   $926.05,   $38.55;  and  withdrew  as  fol- 
lows:    $32.75,    $42.80,    $91.25,    $10.35,    $18.75,    $31.25,    $48, 
$82.15.     What  was  his  balance  in  bank  ? 


72  MODERN    BUSINESS    ARITHMETIC 

Multiplication  and  Division 

223.     To  Multiply  or  to  Divide  United  States  money,  pro- 
ceed as  in  multiplication  or  division  of  decimals. 

.224.     Solve  the  following  : 
1.     Multiply  $125.75  by  47        6.     $25.625  X  11  -*-  25  =  ? 


2.  Multiply  $204.05  by  308  7.  $142.50  +•  12£  X  65  *=  ? 

3.  Divide  $625.75  by  15  8.  $87.75  X  14  —  $54  ==  ? 

4.  Divide  $1875.50  by  12i  9.  $271.25  •+•  .33J  +  $71  = 

5.  Divide  $274.50  by  16f  10.  $95.40  X  48^  —  $172  =  ? 


PRACTICAL  PROBLEMS 

Solve  the  following : 

1.  .  Bought  1248  pounds  of  prunes  at  4  cents  per  pound,   590 
pounds  of  pears  at  5  cents  per  pound,  1892  pounds  of  peaches  at 
3/4  cents  per  pound,  and  636  pounds  of  plums  at  6  cents  per 
pound.     Find  the  total  amount  of  the  bill. 

2.  Jones's  income  was  $1250  per  year.     He  spent  $17  per 
month  for  board,  $135  for  clothes,  $17  for  shoes,   $3  per  month 
for  lodge  dues,  75  cents  per  week  for  washing,  and  $95  for  sun- 
dries.    How  much  did  he  have  left  to  place  in  the  bank? 

3.  Henry's  salary  for  January  was  $35  ;  this  was  increased 
$5  every  month  in  the  year.     What  was  his  total  earnings  for 
the  year  ? 

4.  If  it  cost  7  cents  per  pound  to  raise  hops,  what  will  be 
the  profit  on  a  hop  crop  of  250  bales,  weighing  275  pounds  each, 
sold  at  13/4  cents  per  pound? 

5.  A  merchant  bought  corn  at  55  cents  per  bushel,  wheat  at 
90  cents  per  bushel,  and  barley  at  75  cents  per  bushel.     If  he 
bought  two  bushels  of  wheat  to  every  one  of  barley,   and  two 
bushels  of  corn  to  every  one  of  wheat,  what  was  the  number  of 
bushels  of  each  if  he  paid  $522.50  for  the  whole? 


Simple  Interest 


225.  Interest  is  the  sum  paid   for  the  use  of    money  cr 
other  value.  .  . 

226.  Principal  is  the  money  or  value  for  the  use  of  which 
interest  is  paid. 

227.  Rate  is  the  number  of  cents  paid  for  the  use  of  $1    for 
one  year,  and  is  called  rate  per  cent. 

228.  Bank  Discount    is  the  amount   charged  by  banks 
on  promisory  notes  or  other  commercial  paper  bought  by  the 
bank. 

229.  Interest  and  Bank  Discount  are  estimated  at  a  cer- 
tain rate  on  the  $1. 

230.  To  Find  Interest  or  Bank  Discount  by  the 
Cancellation  Method. 

Write  the  principal,  time,  and  rate  at  the  right  of  a  vertical  line; 
at  the  left  of  this  line  write  a  year  in  the  same  denomination  in 
which  the  time  is  expressed.  Cancel  and  reduce.  The  result  will 
be  the  interest  for  the  given  time  and  rate. 

EXAMPLE  :     Find  the  interest  on  $720  for  7  months  at  6%. 

360     \ 

mo.    7  mo. 
.00  rate 


$25.20  =  Interest 

EXAMPLE  :     Find  the  interest  on  $960  for  63  days  at  8%;  also 
on  $1200  for  1  year  3  months  24  days  at  7  %• 


$00  ds. 


192 


$000 


7  ds.  X$  mo. 

rate 


100 


15.8  mo. 
.07  rate 


$13.44  =  Interest  $110.600  ==  Interest 

1  year  =  12  months.  24  days  =  .8  of  a  month.  Every  3  days 
—  .1  of  a  month. 

NOTE — In  the  above  examples  it  will  be  noticed  that  the  7  months,  the 
63  days,  and  the  15.8  months  are  ^,  /A,  and  V/  of  a  year  respectively, 
and  that  we  are  only  taking  those  fractional  parts  of  a  whole  year's  in- 
terest which  is  always  found  by  multiplying- the  PRINCIPAL  by  the  RAT  E. 
For  further  discussion  of  the  subject  of  interest  see  main  topic. 


74  MODERN    BUSINESS  ARITHMETIC 

231.     Find  the  interest  on  the  following : 

1.  $840  for  30  ds.  at  6%         6.  $150  for  4  mo.  at  6% 

2.  $1230  for  54  ds.  at  6%       7.  $750  for  7  mo.  at  1% 

3.  $1350  for  37  ds.  at  8%       8.  $1050  for  11  mo.  at  7\-% 

4.  $2700  for  93  ds.  at  7%       9.  $325. 50  for  1  yr.  2  mo.  al 

5.  $3500  for  17  ds.  at  9%     10.  $4500 for  5  mo.  12 ds.  at  10% 


PRACTICAL  PROBLEMS 
232.     Solve  the  following  : 

1.  Find  the  interest  on  a  $630  note  for  1  year  4  months  15 
days  at  6  % . 

2.  Find  the  proceeds  of  a  note  sold  at  the  bank  ;  face  of  note, 
$420  ;  time  to  run,  3  months  ;  money  worth  7%. 

3.  Find  the  discount  at  8  %  on  a  note  for  $960  sold  at  bank 
7  months  21  days  before  maturity. 

4.  What  were  the  proceeds  of  a  note  for  $720  discounted  at 
bank  for  105  days  at  7%  ? 

5.  A  $500  note,  with  interest  at  6%,  is  given  for  2  years  8 
months  27  days.     How  much  is  due  at  maturity  ? 

6.  Find  the  proceeds  of  a  note  for  $600,  due  in  1  year,  at  6% 
interest,  discounted  at  bank  4  months  before  due  at  10%. 

NOTE — Discount  the  AMOUNT  of  the  note  at  MATURITY  for  the  time 
yet  to  run. 

7.  How  much  would  be  due  at  maturity  on  Boyd's  note  for 
$1000  given  for  2  years  4  months  27  days  at  6%  ? 

8.  What  would  be  the  proceeds  of  the  above  note  if  sold  at  a 
bank  and  discounted  1  year  2  months  15  days  before  maturity  at 
10%? 

9.  After  holding  a  note  of  $1000,  due  in  2  years  with  inter- 
est at  7%,  for  6  months,  I  sell  it  to  the  bank  at  a  discount  of  9% 
for  time  yet  to  run,  paying  a  collection  fee  of  /^%.     How  much 
should  I  receive?     (  Collection  is  charged  on  face  of  note.) 

10.  The  following  note  was  discounted  at  the  bank  July  25, 
1907  ;  rate  of  discount,  8%: 

$524.50  San  Francisco,  Cal.,  December  10,  1906. 

One  year  after  date  I  promise  to  pay  A.  L.  Ward, 
or  order,  Five  Hundred  Twenty -four  5%oo  Dollars,  with 
interest  at  six  per  cent  per  annum. 

fohn  W.  Wilson. 

If  a  collection  fee  of  ^  %  is  charged,  what  should  be  the  net 
proceeds  of  the  above  note  on  date  of  discount  ? 


SIMPLE  INTEREST 


75 


HOME  WORK— No.  9 

1.  Add  10  Eagles,  540  dimes,  350  cents,  182  mills,  6  dollars, 
135  Eagles,  25  dimes,   5235  cents,   9840  mills,   400  mills,    1725 
cents  and  3  Eagles. 

2.  From  1847.5  dimes  take  15740  mills. 

3.  If  John  received  1  dime,  2  cents,  and  5  mills  per  hour  for 
his  labor,  and  works  11  months,  of  26  days  each,    at  that  rate; 
how  much  will  he  earn  if  he  averages  8.5  hours  each  day  ? 

4.  Find  the  net  proceeds  of  the  following  note,  sold  to  bank 
November  16,  1907,  at  8%  discount: 


5.     Find  the  net  proceeds  of  the  following  note,  discounted  at 
bank  April  26,  1908.     Rate  of  discount,   10%  ;  collection,  *4%  : 


NOTE— The  cancellation  method  of  calculating-  interest  and  bank  dis- 
count here  given  will  enable  students  to  work  out  all  ordinary  problems 
occuring  in  their  business  practice. 


76  MODERN  BUSINESS  ARITHMETIC 

6.  A  note  for  $1272  dated  July  5,  1907,  and  drawing  7%   in- 
terest,  is  paid  September  1,    1908.     What  amount  will  be  re- 
quired to  make  settlement  in  full  ? 

7.  Jones  owed  $7800  unpaid  amount  on  his  farm  which  he 
agreed    to  pay  in  three  equal  yearly  installments  as  follows : 
$2600,  at  8%  interest,  due  in  1  year  ;  $2600,  at  7%  interest,  due 
in  2  years;  and  $2600,  at  6%  interest,   due  in   3   years.     What 
was  the  total  amount  paid  ? 

8.  Matthews  &  Co.  owed  their  jobber  as  follows  : 

Jan.    1,  Mdse.,  $480  bought  on  3  mo.  time. 
Feb.   1,       "          600  1 

Mar.  1,  900  '    2    ' 

If  this  account  is  all  paid  on  May  1 ,   how  much  cash  will  be 
required,  money  being  worth  8%  ? 

9.  Having  on  hand  a  note  for  $1845  due  in  1  yr.   4  mo.   18 
ds.  with  interest  at  6%,  I  sell  it  at  the  bank  7  mo.  24  ds.   before 
due.     If  the  bank  charges  me  8%  discount  and   #%   for  collec- 
tion, how  much  should  I  receive  for  the  note  ? 

10.     Ross  gave  his  note  as  follows  : 

$1254.60  Oakland,  Cal.,July  25,  1908. 

Sixtv  days  after  date  I  promise  to  pay  A.  B.  Glenn,  or  order, 
Twelve  hundred  fifty -four  6%oo  Dollars,  without  interest.  Value 
received. 

KEMP  ROSS. 

What  is  due  on  this  note  December  23,  1908  ? 

NOTE — The  legal  rate  in  California,  when  no  rate  is  agreed  upon,    is 
seven  per  cent. 


Aliquot  Parts 

233.  The  Aliquot  Parts  of  a  number  are  the  fractional 
parts  of  it.     Thus,  2,  3,  4,  6,  9,  12,  and  18  are  aliquot  parts  of 
the  number  36. 

234.  All  composite  numbers  contain  aliquot  parts.     The  ali- 
quot parts  of  100  and  of  360  are  those  most  commonly  used. 

235.  Aliquot  Parts  of  100  : 

50  i  of  100  81  ==  !!2  of  100 

33J  i  of  100  6J  ==  iV  of  100 

25  t  of  100  6t  =  TV  of  100 

20  i  of  100  5    =  ^VoflOO 

16|  J  of  100  4      =  A  of  100 

14?  =    |  of  100  3J  ==  uV  of  100 

124  i  of  100  2i  ==  -?V  of  100 
Hi  i  of  100  2    =  A  of  100 
10  -  -A  of  100  If  ==  ^  of  100 
9-iV  =  IT  of  100  1J  =  ¥V  of  100 

236.  Multiples  of  the  Aliquot  Parts  of  100  : 

66§==4oflOO  87i=    |  of  100 

75    =  |  of  100  18}  =;  A  of  100 

40    =fcflOO  31t==AoflOO 

60    =  |  of  100  43f  ==  TV  of  100 

80    =  |  of  100  56t.=  =AoflOO 

83i  =  |  of  100  68f  =  -H  of  100 

37i  =  I  of  100  81t  ==  II  of  100 

62^  ==  f  of  100  93f  ==  if  of  100 

237.  An  Aliquot  Part  More  or  Less  than  100: 

150      =  i  more  than  100  95      =  A  less  than  100 

133i  ==  t  more  than  100  90      --  ^  less  than  100 

125  =  t  more  than  100  83 i  =      )  less  than  100 
120      =  t  more  than  100  80  t  less  than  100 
ll(>;i  =  i  more  than  100  75    =    t  less  than  100 


78  MODERN  BUSINESS  ARITHMETIC 


=  t  more  than  100  66|  =  t  less  than  100 
110  =  TV  more  than  100  62^  =  f  less  than  100 
108t  =  IT  more  than  100  37i  =  f  less  than  100 

238.  Aliquot  Parts  of  360: 

180  =  i  of  360  40  =  t  of  360 

120  =  t  of  360  36  ==  TV  of  360 

90  =  i  of  360  30  =  iV  of  360 

72  =  t  of  360  24  =  TV  of  360 

60  =  t  of  360  .              20  —  TV  of  360 

45  =  t  of  360  18  ==  TV  of  360 

NOTE — The  aliquot  parts  of  360  days  are  much  used  when   computing 
interest 

239.  To  Find  the  Cost  when  the  Price  or  Quantity 
is  an  Aliquot  Part  of  100. 

Take  such  a  part  of  the  quantity  or  price  as  the  price  or  quantity 
is  a  part  of  100. 

EXAMPLE  :     What  will  be  the  cost  of  887  yards  of  cloth  at  33J 
cents  per  yard  ? 

At  $1.00  per  yd.  387  yds.  would  cost  $387. 

At  33J  cents  per  yd.  the  cost  will  be  i  of  $387  =  $129. 

240.  Find  the  cost  of  the  following  invoices,  making  all  ex- 
tensions mentally : 

1.     480#  Cocoa  50^  2.     368  yds.  Cabot  A 

270#  Japan  Tea  33i^  711  yds.  Cabot  W 

325#  Sugar  5^  515  yds.  Muslin 

840#  Rice  12^  948  yds.  Linings 

918#  Raisins  16f^  425  yds.  Gingham 

385#  B.  Powder  20^  432  yds.  Cambric 


3.     24  bxs.  Soap  87i#        4.     6  doz.  cans  Corn 

120#  Starch  20^  4  doz.  cans  Beans 

48  gals.  Molasses  37^^  10  doz.  cans  Peas 

"  32  gals.  Vinegar  18|^  15  doz.  cans  Oysters 

320#  Salt  lj^  7  doz.  cans  Clams 

28#  Pepper  25^  2  doz.  cans  Lobsters 

16#  Spice  12i^  2  doz.  cans  Shrimps 


ALIQUOT  PARTS  79 

5.   12  doz.  qts.  Peaches       10^       6.   240  sks.  Flour          $1.12* 

8  doz.  qts.  Pears              8^  80  sks.  Graham  .37$ 

6  doz.  qts.  Plums          12-J^  72  sks.  Corn  Meal  .62| 

6  doz.  qts.  Apricots        150  48  sks.  Rye  Flour  .83{ 

12  doz.  qts.  Cherries    16§^  48  sks.  Buckwheat    1.081 

10  doz.  qts.  Blackbrs.     6|^  24  sks.  Hominy  1.25 

10  doz.  qts.  Loganbrs.   8\0  36  sks.  Potatoes  1.15 

12  doz.  qts.  Strawbrs.  12|f  18  sks.  Beans  3.50 

241.  To  Find   the  Price  or  Quantity   when    the 
Quantity  or  Price  is  an  Aliquot  Part  of  100. 

Divide  the  cost  by  the  quantity  or  price  by  dividing  it  by  the  Al- 
iquot part  the  the  quantity  or  price  is  of 100. 

EXAMPLE  :     At  12^  cents  per  yard,  how  many  yards  of  cloth 
can  be  bought  for  $60  ? 

12i  =  i  of  100.      60  -f-  i  =  60  X  8  =  480,  No.   of  yards. 

242.  Find  the  price  or  quantity  of  each  of  the  following  by 
multiplication  only  : 

1.  At  25  cents  per  yd.,   how  many  yds.   of  flannel   can   be 
bought  for  $35  ? 

2.  At  33j  cents  per  bushel,  how  many  bushels  of  oats  can  be 
bought  for  $127  ? 

3.  At  16|  cents  per  lb.,   how  many  Ibs.    of  cheese  can   be 
bought  for  $52.50? 

4.  Bought  12|  yds.  of  cloth  for  $17.75.     What  was  the  price 
per  yd.  ? 

5.  At  8j  cents  per  doz.,  how  many  doz  eggs  can  be  bought 
for  $4.50? 

6.  At  $1.25  per  yd.,  how  many  yds.  of  silk  can  be  bought 
for  $37. 50? 

7.  Bought    62^  bushels  of  millet  for  $225.     What  was  the 
price  per  bushel  ? 

8.  At  83J  cents  per  yd.,   how  many  yds.   of  carpet  can  be 
bought  for  $120? 

9.  At  .14 1  cents  each,  how  many  books  can  be  bought  for 

$88? 

10.     Sold  my  farm  of  66 §  acres  for  $7500.     What  was  the  price 
per  acre  ? 


80 


MODERN  BUSINESS  ARITHMETIC 


HOME  WORK— No.  10 


Extend  and  foot  the  following 


1.                                            2. 

3. 

75  yds.  @  $.50               96  Ibs.  @ 

$.01}                189  yds.  @  $.66} 

88  yds.  @     .09^            56  Ibs.  @ 

.02}                256  yds.  @     .18f 

91  yds.  @     .14f             76  Ibs.  @ 

.05                  528  yds.  @     .75 

72  yds.  @     .12}             75  Ibs.  @ 

.06|                728  yds.  @     .87} 

78yds.  @     .16}             84  Ibs.  @ 

'     .08}                 616  yds.  @     .62} 

96  yds.  @     .25               90  Ibs.  @ 

.01|                775  yds.  @     .60 

84  yds.  @     .33}             80  Ibs.  @ 

.06}                952  yds.  @     .37} 

99yds.  @     .11}             87  Ibs.  @ 

.03}                 648  yds.  @     .83} 

4,                                            5. 

6. 

176  yds.  @  $.31}         1424  prs.  <£ 

g  $1.50            1656  gal.  @  $  .13} 

432  yds.  @     .81}         2562  prs.  <g 

g     1.33}         2454  gal.  @     2.16} 

592  yds.  @     .43f         1728  prs.  <£ 

I     1.83}         3144  gal.  @     1.11} 

678  yds.  @     .16}         2436  prs.  <£ 

g       .95  .         4215  gal.  @    3.33} 

816  yds.  @     .56}         7648  prs.  | 

g     1.25           7544  gal.  @     2.12} 

904  yds.  @     .62}         7734  prs.  <g 

g     1.16}         7776  gal.  @       .15} 

945  yds.  @     .28f         8425  prs.  <g 

g     1.20            8592  gal.  @     1.17} 

972  yds.  @     .83}         9236  prs.  | 

g     2.25           8979  gal.  @       .34} 

Find  the  total  quantity  of  the 

following  : 

7. 

8. 

Cost  $14,  price  per  Ib.  $.25 

Cost  $35,  price  per  yd.  $  .66} 

Cost    37,  price  per  Ib.     .33} 

Cost    44,  price  per  yd.     1.25 

Cost    54,  price  per  Ib.     .16} 

Cost    56,  price  per  yd.     1.33} 

Cost    67,  price  per  Ib.     .12} 

Cost    64,  price  per  yd.       .87} 

Cost    72,  price  per  Ib.     .08} 

Cost    72,  price  per  yd.       .37} 

Cost    83,  price  per  Ib.     .14f- 

Cost    84,  price  per  yd.     1.12} 

Cost    86,  price  per  Ib.     .11} 

Cost    96,  price  per  yd.     1.16} 

Cost    91,  price  per  Ib.     .06} 

Cost    38,  price  per  yd.     1.18f 

Find  the  price  of  each  of  the  following  : 

9. 

10. 

Cost  $480.00,  quantity  1440  yds. 

Cost  $112.00,  quantity    336# 

Cost    594.00,  quantity  2376  yds. 

Cost      67.20,  quantity    672# 

Cost    512.50,  quantity  3075  yds. 

Cost    107.50,  quantity    430# 

Cost    312.25,  quantity  2498  yds. 

Cost      31.20,  quantity    936# 

Cost    416.00,  quantity  2912  yds. 

Cost    144.00,  quantity    192# 

Cost    667.00,  quantity  4002  yds. 

Cost      46.00,  quantity    552# 

Cost    743.25,  quantity  5946  yds. 

Cost      88.00,  quantity    528# 

Cost    855.75,  quantity  3423  yds. 

Cost    233.40,  quantity  1167# 

ANALYSIS 

243.  Analysis  in  arithmetic  is  the  mental  separation  of  a 
problem  into  its  elements  to  obtain  definite  results. 

244.  The  Unit  is  the  basis  of  all  arithmetical  analyses. 

245.  In  Simple  Analysis  there  is  always  one  step;  viz., 
to  reduce  from  the  unit,  or  to  the  unit. 

EXAMPLE  :     If  one  hat  costs  $3,  what  will  four  hats  cost? 

ANALYSIS  :     If  ONE  hat  costs  $3, 

FOUR  hats  will  cost  4  times  $3,  or  $12. 

EXAMPLE  :      If  five  hats  cost  $15,  what  will  one  hat  cost? 

ANALYSIS  :     If  FIVE  hats  cost  $15, 

ONE  hat  wil  cost  £  of  $15,  or  $3. 

246.  In    Compound  Analysis    there  are  always  two  or 
more  steps;  viz.,  to  the  unit,  and  from  the  unit. 

EXAMPLE  :     (  a  ).   If  5  hats  cost  $15,  what  will-7  hats  cost? 

ANALYSIS  :     If  FIVE  hats  cost  $15, 

ONE  hat  will  cost  \  of  $15,  or  $3  (to  the  unit),  and 
SEVEN  hats  will  cost  7  times  $3,  or  $21  (from  the  unit). 

EXAMPLE:     (£).   If  %  of  a  ton  of  hay  cost  $12,   what  will 
%  of  a  ton  cost  ? 
ANALYSIS  : 

If  f  of  a  ton  cost  $12, 

I  of  a  ton  will  cost  J  of  $12,  or  $3  (to  the  fractional  unit),  and 
g,  or  1  ton,  will  cost  5  times  $3,  or  $15  (to  the  unit). 
If  I ,  or  1  ton  costs  $15,  then  (from  the  unit) 

\  of  a  ton  will  cost  \  of  $15,  or  $5  (to  the  fractional  unit),  and 
|  of  a  ton  will  cost  twice  $5,  or  $10  (to  the  fraction). 

NOTE — The  discussion  and  problems  in  Analysis  here  given  are  for 
the  purpose  of  developing  the  reasoning  faculties.  The  amount  of  work 
is  purposely  limited  that  the  student  may  feel  that  he-  has  time  to  com- 
plete it  in  a  most  thorough  manner. 


247.     Comparison  of  Whole  Numbers. 

1.     If  7  coats  cost  $84,  what  will  11  coats  cost? 

ANALYSIS  :     If  7  coats  cost  $84,  one  coat  will  cost  I  of  $84,  or  $12,  and 
11  coats  will  cost  11  times  $12,  or  $132. 


82  MODERN    BUSINESS    ARITHMETIC 

2.  If  13  hats  cost  $39,  what  will  9  hats  cost  ? 

3.  If  11  pairs  of  shoes  cost  $49.50,  what  will  15  pairs  cost? 

4.  If  7  men  can  do  a  piece  of  work  in  15  days,  how  long  will 
it  take  10  men  to  do  it  ? 

5.  If  3  men  cut  12  cords  of  wood  in  6  days,  how  many  days 
will  it  take  4  men  to  cut  8  cords  ? 

6.  If  $240  will  pay  the  board  of  6  persons  for  4  weeks,   for 
how  many  weeks  will  $540  pay  the  board  of  9  persons  ? 

7.  If  4  men  can  mow  24  acres  of  grass  in  3  days,   how  long 
will  it  take  6  men  and  4  boys  to  mow  40  acres  if  one  man  can  do 
as  much  as  two  boys  ? 

8.  If  an  automobile  can  travel   1550  miles  in  5  days  of  10 
hours  each,  how  far  can  it  go  in  8  days  of  12  hours  each? 

9.  Brown  employs  45  men  to  do  a  job  of  work  in  3  months  ; 
wishing  to  complete  the  work  in  2Vz  months,  how  many  addition- 
men  would  be  required  ? 

10.  If  a  block  of  granite  12  feet  long,  4  feet  wide,  and  15 
inches  thick  weighs  6480  Ibs.,  what  will  be  the  weight  of  a  simi- 
lar block  15  feet  long,  5  feet  wide,  and  2  feet  thick  ? 


248.     Comparisons  Having  Fractional  Numbers. 

1.  James  lost  12  marbles  which  was  %  of  what  he  had  at 
first.     How  many  had  he  at  first  ? 

ANALYSIS  :     If  12  marbles  is  f  of  what  James  had  at  first,  |  is  -J  of  12 
marbles, or  4  marbles,  and  f  is  8  times  4  marbles,  or  32  marbles. 

2.  If  7  yards  of  cloth  cost  $21,  what  will  %  of  a  yard  cost? 

3.  If  %  of  a  ton  of  hay  costs  $7.50,  what  will  8  tons  cost  ? 

4.  If  %  of  a  barrel  of  vinegar  costs  $5.25,  what  will  His  of 
a  barrel  cost  ? 

5.  If  %  of  %  of  an  acre  of  land  is  worth  $16.50,  what  is  the 
value  of  %  of  %  of  an  acre  ? 

6.  What  number  is  it  that  if  you  add  %  of  itself  the  result  is 
135? 


ANALYSIS    •  83 

7.  A  young  lady  being-  asked  her  age  replied  :     "  If  to  my 
age  you  add  Vs  and  %  of  my  age,  the  sun>  is  26  years."     What 
was  her  age  ? 

8.  The  sum  of  two  numbers  is  35  ;  their  difference  is  l/2  the 
less  number.     What  are  the  numbers? 

9.  What  part  of  3  is  %  of  2  ? 

10.  A  boy  lost  Vs  of  his  kite  string  and  then  added  60  feet 
more,  when  he  found  he  had  %  as  much  as  at  first.  What  was 
the  original  length  ? 


249.  Partnership  Problems. 

1.  If  A  invests  $200,   and  B  $500,    and  their  total  gain  is 
$210,  how  much  of  the  gain  should  each  receive? 

ANALYSIS  :  If  A  invests  $200,  and  B  $500,  their  total  investment  is 
$700,  of  which  A's  share  is  f ,  and  B's  share  is  \.  Their  total  gain  is  $210, 
and  since  their  gain  is  in  proportion  to  their  capital,  A's  share  is  \  of 
$210,  or  $60,  and  B's  share  is  f  of  $210,  or  $150. 

2.  A  invests  $3000,   B  $4000,   and  C  $5000.     If  their  total 
loss  is  $840,  what  should  be  each  one's  share? 

3.  Jones    invests   $300   for   5  months;    Brown,   $400    for    4 
months  ;   and  Smith,  $700  for  2  months.     If  their  total  gain  is 
$405,  how  much  should  each  receive? 

4.  The  total  gain  of  a  firm  was  $770.     White  puts  in  %  the 
capital  for  7  months,  Green  Vs  the  capital   for   12   months,    and 
Black  the  remainder  for  10  months.     How  much  was  each  one's 
share  of  the  gain  ? 

5.  Hill,  Cooper,  and  Sullivan  are  partners  in  business.     Hill 
puts  in  $400  for  7  months  and  gains  a  certain  sum  ;  Cooper  puts 
in  $700  for  a  certain  time  and  gains  $105  ;  Sullivanputs  in  a  cer- 
tain sum  for  2  months  and  gains  $90.     If  the  total  gain  of  the 
firm  is  $335,  what  is  Hill's  gain,   Cooper's  time,  and  Sullivan's 
capital  ?  

250.  Labor  Problems. 

1.  If  A  can  do  a  piece  of  work  in  3  days  and  B  in  5  days, 
how  long  will  it  take  them  to  do  it  working  together  ? 


84  MODERN    BUSINESS    ARITHMETIC 

ANALYSIS  :  If  A  can  do  the  work  in  3  days,  he  can  do  £  of  it  in  1  day. 
If  B  can  do  it  in  5  days,  he  can  do  J  of  it  in  1  day.  Both  working  to- 
gether can  do  the  sum  o£  £  and  I,  or  T8f  of  it  in  1  day,  and  to  do  £f,  or 
all  the  work,  will  require  as  many  days  as  T8S  is  contained  in  |f,  or  1| 
days. 

2 .  Lambert  can  saw  a  certain  pile  of  wood  in  8  days  ;   Lewis 
in  12  days,  and  Lucien  in  6  days.     How  long  will  it  take  all 
three  to  do  it? 

3.  Two  men  can  dig  a  ditch  in  15  days.    The  first  can  dig  it 
alone  in  in  25  days.     How  long  will  it  take  the  second  to  dig  it 
alone  ? 

4.  A,  B,  and  C  can  do  a  job  of  work  in  three  days.     A  can 
do  it  in  9  days  ;  B  in  12  days.     How  long  will  it  take  C  to  do 
the  job  ? 

5.  Ralph  can  mow  a  field  in  4  days,  'and  Lewis  can  mow  it 
in  6  days.     How  long  will  it  take  Ralph  to  finish  the  work  after 
they  have  both  worked  together  1  day  ? 


251.     Time  Problems. 

1.  What  is  the  time  of  day,  if  the  time  past  noon  equals  Vs 
the  time  to  midnight  ? 

2.  What  is  the  time  of  day  if  %  the  time  to  noon  equals  the 
time  past  midnight  ? 

3.  What  is  the  time  of  day  if  Vs   the   time   past   midnight 
equals  the  time  to  midnight  again  ? 

4.  What  is  the  time  of  day  if  %  the  time  past  noon  equals  Vs 
the  time  to  midnight  ? 

5.  What  is  the  time  of  day  if  %  of  the  time  past  midnight 
equals  %  the  time  to  midnight  again  ? 


252.     Clock  Problems. 

1.  How  many  minute  spaces  does  the  minute  hand  gain  on 
the  hour  hand  every  hour  ? 

ANALYSIS  :  If  the  minute  hand  travels  60  minute  spaces  in  1  hour, 
and  the  hour  hand  travels  5  minute  spaces  in  the  same  period,  the  min- 
ute hand  will  gain  55  minute  spaces  every  hour. 


ANALYSIS  85 

2.  At  what  time  between  1   o'clock  and  2  o'clock  are  the 
hour  and  minute  hands  together  ? 

3.  At  what  time  between  5  and  six  o'clock  are  the  hour  and 
minute  hands  together  ? 

4.  At  what  time  between  3  and  4  o'clock  are  the  hour  and 
minute  hand  in  a  straight  line  ? 

5.  At  what  time  between  7  and  8  o'clock  are  the  hands  of  a 
clock  at  right  angles  ? 


253.    Fish  and  Pole  Problems. 

1 .  The  head  of  a  fish  is  9  inches  long ;  the  tail  is  as  long  as 
the  head  and  half  the  body,  and  the  body  is  as  long  as  the  head 
and  tail  together.     How  long  is  the  fish  ? 

ANALYSIS  :  If  the  tail  is  as  long  as  the  head  (  9  inches  )  and  \  the 
body,  the  head  any  tail  together  are  9  inches  and  9  inches  and  \  the 
body ;  since  the  body  is  as  long  as  the  head  and  tail  together,  the  length 
of  the  head  and  tail  equals  \  the  length  of  the  fish,  and  18  inches  equals 
\  the  length  of  the  body  or  J  the  length  of  the  fish,  72  inches. 

2 .  The  head  of  a  fish  is  6  inches  long ;  the  tail  is  as  long  as 
V2  the  head  and  1A  the  body,  and  the  body  is  twice  the  length  of 
the  head  and  tail  together.     How  long  is  the  fish  ? 

3.  A  pole  stands  6  feet  in  the  water;  Vs  of  its  length  is  in 
the  mud,  and  four  times  as  much  is  in  the  air  as  in  the  mud  and 
water  together.     What  is  the  length  of  the  pole  ? 

4.  A  pole  is  in  four  sections ;  the  first  is  2  feet  long  ;   the 
second  is  as  long  as  the  first  and  half  the  third,  and  the  third  is 
as  long  as  the  first  and  second,  while  the  fourth  is  as  long  as  the 
first,  second,  and  third  together.     How  long  is  the  pole? 

5.  A  liberty  pole  was  broken  off  i  of  its  length  plus  3  feet 
from  the  top ;  the  part  left  standing  was  found  to  be  12  feet 
longer  than  three  times  the  length  of  the  part  broken  off.    What 
was  the  original  length  of  the  pole  ? 


254.    Age  Problems. 

1.     George  is  8  years  old  and  his  father  is  32.     How  long  be- 
fore George  will  be  one-half  the  age  of  his  father  ? 


86  MODERN    BUSINESS    ARITHMETIC 

ANALYSIS:  If  George  is  8  years,  and  the  father  32  years,  the  differ- 
ence of  their  ages  is  24  years.  If  George  is  to  be  \  the  age  of  his  father, 
his  age  will  be  equal  to  the  difference  of  their  ages,  or  24  years.  If  he 
is  now  8  years,  it  will  be  16  years  before  he  is  24  years  old. 

2.  One-third  .of  A's  age  equals  three-fourths  of  B's;   and  the 
sum  of  their  ages  is  52  years.     How  old  is  each  ? 

3.  Two-thirds  of  three-fifths  of  Jones's  age  is  four-fifths  of 
five-sixths  of  Smith's.     If  the  difference    of    their    ages  is   28 
years,  how  old  is  each? 

4.  John  is  three  times  as  old  as  Jack,  but  in  5  years  he  will 
be  only  twice  as  old.     What  is  the  age  of  each? 

5.  Twelve  years  ago  Glover  was  one-fourth  the  age  of  his 
uncle.     Now  he  is  one-half  as  old.     How  old  is  each  ? 


255.    Miscellaneous  Problems. 

1.  A,   B,   and    C    take   luncheon   together.     A   furnishes   4 
loaves,  B  3  loaves,  and  C  pays  35  cents  for  his  share.     If  all  eat 
equal  amounts,   how  should  the  money  be  divided  between  A 
and  B? 

2.  How  far  can  a  person  ride  in  an  automobile,   traveling  at 
the  rate  of  20  miles  an  hour,   and  return  on  his  bicycle  at  the 
rate  of  10  miles  an  hour,  if  he  is  gone  six  hours  ? 

3.  A  hound  is  60  yards  behind   a  fox.     How  far  will  the 
hound  have  to  run  to  catch  the  fox  if  he  runs  10  yards  to  every 
8  of  the  fox,  and  one  leap  of  the  hound  equals  two  of  the  fox's? 

4.  I  sold  a  bill  of  goods  and  gained  20%.     Had  they  cost  me 
$45  more,  I  would  have  lost  10%.     What  was  the  cost  of  the 
goods  ? 

5.  A  and  B  meet  at  a  butcher  shop  and  together  buy  80 
pounds  of  beef,  the  price  of  which  is   10  cents  per  pound.     A 
takes  50  pounds  of  the  better  quality,  and  agrees  to  pay  one-half 
cent  more  per  pound  than  B  does  for  the  remainder.     How  much 
shall  each  one  pay  ? 


ANALYSIS  87 

HOME  WORK-NO.  11 

NOTE— Students  should  take  much  pride  in  making  out  a  full  set  of 
problems,  together  with  solutions,  as  indicated  by  the  following  outline  : 

1.  Give   original  examples,   with  .solutions,   illustrating  the 
different  steps  in  simple  analysis. 

2.  Give  original  examples,  with  complete  analyses,  showing 
the  different  steps  in  compound  analysis. 

3.  Originate  a  problem  in  the  comparison  of  whole  numbers, 
using  not  less  than  five  integers. 

4.  Originate  a  problem  in  the  comparison  of  fractional  num- 
bers, using  not  less  than  two  fractions  and  as  many  whole  num- 
bers as  necessary. 

5 .  Refer  to  Article  249  and  then  write  out  a  partnership  prob- 
lem in  which  the  capital  and  time  of  each  partner  are  different. 

6.  Write  a  labor  problem  entirely  unlike  those  given  in  Arti- 
cle 250. 

7.  Originate  a  time  problem,  using  time  past  noon  and  time 
to  noon  similar  to  those  in  in  Article  251. 

8.  Originate  a  clock  problem,  giving  in  degrees  the  angle  des- 
cribed by  the  hands  of  the  clock. 

9.  Originate  a  fish  and  pole  problem. 
10.     Write  an  original  age  problem. 


Bills,  Invoices,  and  Statements 


256.  A  Bill  or  Invoice  is  an  itemized  statement  of  goods 
bought  or  sold.     The  term  Bill  is  also  applied  to  any  itemized 
statement  of  material   furnished,    labor   performed,   or  services 
rendered. 

257.  The  term  Invoice  is  usually  applied  to  bills  of  consider- 
able value,  and  containing  several  or  many  items. 

258.  A  Bill  should  contain  the  following  : 

1.  The  place  and  date. 

2.  The  name  and  address  of  the  buyer. 

3.  The  name  and  address  of  the  seller. 

4.  The  terms  of  sale. 

5.  The  quantity,  price,  and  extension  of  each  item. 

6.  The  total  amount,  or  footing. 

INTEREST  CHARGED   AT  1O   PER  CENT.  PER  ANNUM    ON   ALL   ACCOUNTS   AFTER    MATURITY 

HOOPER  &  JENNINGS 

Importers  and  Wholesale  Grocers 

462-464  Bryant  Street 

San  Francisco,  Cal.,        July  20,  1908. 
Sold  to    W.  E.  GIBSON,  Oakland,  Cal.  TERMS  60  DAYS 


2ff 


ff 


259.     Bills  may  be  receipted  in  full,  or  credits  given  for  partial 
payments. 


BILLS,  INVOICES,  AND  STATEMENTS 


89 


260.     To  Receipt  a  Bill  is  to  write  upon  it  an  acknowledg- 
ment of  payment  signed  by  the  seller. 


TERMS  •     30  days 


SAN  FRANCISCO  CAL.,      Feb.  4,  1908. 

Bowen  &  Goldberg 

WHOLESALE  GROCERS 

Main  Office:     No.  J732  Market  Street 


SOLD  TO  E.  K.  ISACCS,  Los  Angeles,  Cal. 

SUBJECT  TO  SIGHT  DRAFT  WHEN  DUE.  INTEREST  CHARGED  AFTER  MATURITY. 


CORRECT  PROPORTIONS 
PERFECT  FINISH 


THOROUGH  WORKMANSHIP 
UNION  MADE 


C.  J.  HBBSEMAN 

Makers  of  Workingmen's  Best  Garments 

FACTORY  I 

1107-9-11-13  WASHINGTON  STREET 

PHONE  MAIN  678 
Sold  to      KEEGAN  BROS. 

TERMS  NET  30  DAYS  Oakland,  Cal.,      March  29,  1908. 


45 

1 

doz.  Com.  Suits 

9 

00 

12 

1 

'  Plasterers'  Overalls 

6 

50 

31 

1 

'  White  Aprons 

6 

50 

21 

2 

'  Coats             9.50 

19 

00 

20 

4 

'  Eng.  Overalls      9.50 

38 

00 

42 

1 

'  Blk.  Golf  Shirts 

6 

00 

85 

00 

) 

- 

90 


MODERN  BUSINESS  ARITHMETIC 


261.  To  Discount  a  Bill  is  to  make  an  allowance  from 
the  list  price  either  to  obtain  the  selling  price  or  to  induce  the 
buyer  to  pay  the  bill  before  it  is  due. 


F.  0.  GARDINER,  Stockton,  Cal. 


Chicago,          May  2,  1908 


BOUGHT   OF 


The  Gregg  Publishing  Company 

1512      WABASH       AVENUE 

TERMS  CASH.    Remittances  must  be  made  in 

postal  or  express  money  order,  or  in  bank  draft. 

Personal  checks  upon  local  banks  not  received 

unless  exchange  rates  are  added. 


262.     Several  discounts  are  some  times  offered  on  one  bill,  the 
terms  being  indicated  on  the  bill  head. 


TERMS  : 
60ds.net;  30  ds.  5%;  10  ds. 


San  Francisco^    April  4,  '08 


L.  B,  LAWSON  &  CO. 

China,  Glass,  and  Earthenware 

Chicago,  Illinois* 

Sold  to   A.  P.  ARMSTRONG,  Portland,  Oregon 


€fe**> 

S3- 

.^r^^L^>^  -~tL£^^^^ 

/^  -^ 

^X/ 

3-  *-S 

7s  ^^A^JUM^ 

4S^f~ 

JH 

SI     ^^^^^rtS^'tt**^ 

^/ 

*SJ 

rj9^>. 

iC 

//^5L^£^/  HB^^_ 

13- 

f-J 

„ 

/i      ^^A/^X      ^^^       £Z~^ 

//* 

•>* 

•Lstt-*. 

*</ 

x 

s  " 

V--'?^e2^>^X^-x  /2-/(^-S   fr  7* 

TzZ&^sSZ*^ 

M^jft^ 

^^j 

^~—            ~^~-~ 

BILLS,  INVOICES,  AND  STATEMENTS 


91 


263.  A  Statement  is  a  summary  of  invoices  sold,  together 
with  any  credits  allowed,  and  showing  the  balance  remaining 
unpaid. 


STATEMENT 


April  1,  1908 


2?il?rbarlj  $Iap?r  (Eompattg 


J.  S.  Sweet  Publishing  Co.,  Santa  Rosa  Cal. 


264.     A  Credit  Memorandum  is  given  when  goods  are  re- 
turned or  when  a  claim  against  a  bill  for  some  cause  is  allowed. 


CREDIT  MEMORANDUM 

American  Type  Founders  Co. 

820  Mission  Street, 

SAN  FRANCISCO,      April  13    1908 

J.  S.  Swe et  Pub.  Co.,  Santa  Rosa 


Rebate  on  bill  April  1,  '08 

3 

15 

92 


MODERN  BUSINESS  ARITHMETIC 


265.  To  Extend  the  items  of  a  bill  is  to  multiply  the  price 
of  one  by  the  number  and  to  write  the  result  in  the  first  money 
column. 

266.  Short  Extension  is  the  placing  of  several  items  on 
the  same  line,  extending  only  their  sum  to  the  money  column. 

San  Francisco.        Feb.  5,  1908. 
A.  M.  GROUSE,  Santa  Rosa 

TO  SMITH'S  CASH  STORE DR 


Country  Trade  Solicited 


Retail  Grocers 


QaatZ. 

h? 

±J*-~^yj  "  ^L^^^y  •**  ^fc^^.y^ 

to  I 

/? 

/si,  ^d^/"r"  ^L^^,^^'°  &L  Y  v-^ 

(ZjC 

i£l 

x^^J^r^y  ^-^  j^    ^/  x  —          ^ 

/ 

-rf-<~ 

6 

-T&y/^^y  *"    ^2^  2J~  ^^f^—^jt^.^  7*" 

/ 

n?'<7 

(^                          +°         tj^  (/                    S3"^—^!            ^    •2"rX 

a  a 

7/ 

^^a^Lf^^,^  ^"^  /3^,  ^~  s  ^^  ^^¥L~^  x~ 

A 

s 

7 

-^ 

' 

267.     Commercial  Signs  and  Abbreviations : 


Acct.,  or  %,  account. 

@,  at  or  per. 

Ami.,  amount. 

BaL,  balance. 

Ex.,  Bxs.,  box,  boxes. 

Bo't,  bought. 

TD   / 

/L,  bill  of  lading. 
%>»  in  care  of. 
Co.y  company. 
Ctg.,  cartage. 
Coin.,  commission. 
Contra.,  against. 
Exch.,  exchange. 
C.  O.  D.,  collect  on  delivery. 
For 'd,  forward. 
Cr. ,  credit,  or  creditor. 
Dr. ,  debit,  or  debtor. 
E.  and  O.  E. ,  errors  and  omis- 
sions excepted. 


F.  O.  B.,    or  /.  o.  6.,    free  on 

board. 

Mdse.,  merchandise. 
Net.,  without  further  discount. 
Sunds.,  sundries. 
Rec'd,  received. 
#,  number. 
#,  pounds. 
£,  cent. 
$,  dollars. 
;£,  pounds  sterling. 
% ,  per  cent. 

31  is  read  31A. 

32  is  read  3l/2. 

33  is  read  3%. 
(°),  degrees. 
O,  foot,  feet. 
(r/),  inch,  inches. 
Pkg.,  package. 

L.  P.,  ledger  folio. 


BILLS,  INVOICES,  AND  STATEMENTS 

HOME  WORK— No.  12 

268.     Find  the  cash  cost  of  each  of  the  following  bills : 
1. 


93 


Oakland,  Cal.,  May  18,   1908. 

M      KETTERLIN  BROS.,  Santa  Rosa,  Calif/ 

TO  i!r2Ctttla£-fkrkttts  dompattg  »*• 

MANUFACTURERS    AND    IMPORTERS    OF 

PAINTS,  OII,S,  VARNISHES, 
COLORS,  ETC. 


SAN   FRANCISCO 

707-9-11    SANSOME  STREET 


OAKLAND 

1  7TH  AND  CAMPBELL  STS. 


1 

10 

300 
100 

bbl.  Paris  White-357  Ibs.       .15 
gal.  XX  White-5's            1.00 
Ibs.  MPC  Lead-50's            .062 
'  -15  's            .06 

] 

Chicago,  ILL,  March  15,  '08. 

HART,  SCHAFFNER  &  MARX 

SHAKERS  OF  FINE  CLOTHES  &OR  §MEN 
Van     Buren     and     Market     Streets 


SOLD  TO      KEEGAN  BROS. , 

Santa  Rosa,  California 


SHIPPED  VIA 

Milw.,  viaU.  P. 


TERMS: 


June  1,  '08. 

7%  10  ds.,  5%  30  ds, 


STOCK   NO. 


26552 

7 

Suits            8.50 

26873 

5 

"             15.00 

32738 

5 

"             18.00 

30777 

5 

"             15.50 

29800 

1 

«  t 

16 

00 

27374 

5 

"             14.00 

26606 

1 

t  ( 

15 

50 

27011 

8 

12.00 

26762 

8 

Pants           3.75 

27049 

7 

"             3.50 

27073 

4 

"              3.50 



-? 

94 
3. 


MODERN  BUSINESS  ARITHMETIC 


Jfatttterg  010. 


816-820  Mission  St.,  San  Francisco 

Date  [  March,  5, '08.  ] 
J.  S.  SWEET  PUBLISHING  CO., 


Santa  Rosa,  Cal. 


Shipped. 


Designer  and  Maker  of 
Fashionable    Styles    in 

TYPE 

World's  Largest  Seller 
Everything  for  Printers 

Your  Order  No.  51260 


QUAN- 
TITY 

POINT 

DESCRIPTION 

TYPE                 SUPPLIES 

PER   CENT 
DISCOUNT 

TOTAL 

45# 

5f 

1 

10 
10 
10 
10 

Lin.  Ronaldson  #551    .60 
Quads                                 .45 
Lin.  Ronaldson  Slope  #2 
I.e.         "                " 

2 
1 

50 

15 

list 

1 

18 

Lin.          "          Clarendon 

3 

25 

1 

12 

t  (            it                   it 

2 

75 

1 

8 

ft            1  1                   i  ( 

2 

25 

12# 

10 

Mod.  #510  Figures         .60 

10# 

10 

Spaces  &  Quads               .50 





4 

Yankee  Job  Cases           .75 







10 

1 

Quarter  Cases 

3 

00 

list 

1 

Harris  Rule  Case 

4 

65 

ii 

Less  discount 

— 

— 

Freight  allowance 

— 

— 

— 

25. 

Total 

— 

— 

4. 

SAN  FRANCISCO 


SACKAMKNTO 


Los  ANGELES 


NEW  YORK 


Bought  of  BAKER  &  HAMILTON 

Reg.  NO. —  -   Shipping  NO. San  Francisco,    Apr .  5 , '  08 

Sold  to      KETTERLIN  BROS.  Santa  Rosa 


2 

Sensible  Twine  Holders 

.20 

3 

1 
4 

AAA  J  Wrenches  #15 
doz.  Atkin  Excel  Saw  Tools 

.45 
6.50 

'  '  Bolts  &  Nuts-8i  Shears 

4.50 

2 

Coil  Gal.  Fence  Wire  #16 

3.65 

1 

'  »  Tarred  Lath  Yarn-93  Ib. 

.101 

i 

doz.  Reload  Outfits 

2.80 

2 

Ibs.  Brass  Pins  f  -  16 

.78 

1 

>  »    >  >    i  >  |  -  18 

.94 

9 

Denominate  Numbers 

271.  A  Denominate  Number    is    a    concrete    number 
whose  unit  is  a  measure  ;  as,  5  inches,  10  pounds,  20  hours. 

272.  A  Simple  Denominate  Number  has  but  one  de- 
nomination ;  as,  6  yards. 

273.  A  Compound  Denominate  Number  contains  two 
or  more  denominations  ;  as  6  yards  2  feet  8  inches. 

274.  A  Measure  is  the  unit  of  computation. 

275.  A  Quantity  is  measured  by  the  number  of  times  it 
contains  the  unit  of  measure. 

276.  The  Classification  of  measures  is  as  follows  : 

1.  Value  or  Money  4.     Extension 

2.  Weight  5.     Time 

3.  Capacity  6.     Arcs  and  Angles 


Measures  of  Value 

UNITED  STATES  MONEY 

277.  United  States  Money  is  the  legal  currency  of  this 
country.     The    system    was   adopted   in    1786,    and   has   been 
changed  several  times  by  acts  of  congress. 

278.  'The  Unit  of  measure  is  the  dollar,  and  sums  of  money 
are  spoken  of  as  dollars  and  cents.     The  Eagle  and  dime  are  sel- 
dom mentioned  in  business  transactions. 

TABLE : 

10  mills        =  1  cent ^,  or  ct. 

10  cents       =  1  dime d. 

10  dimes    —  1  dollar.... $. 
10  dollars  ==  1  Eagle.... E. 

NOTE — In  business  transactions,  dollars  and  cents  are  used  with  the 
decimal  point  between;  as,  $17.50. 

NOTE — For  further  discussion  of  this  subject,  see  page  69. 


,  96  MODERN    BUSINESS    ARITHMETIC 

CANADA  MONEY 

279.  Canada  Money  is  the  legal  currency  of  Canada,  and 
has  about  the  same  values  as  the  United  States  money.     Its  unit 
is  the  dollar. 

TABLE  : 

10  mills     =  1  cent,  ^  or  ct. 
100  cents  =  1  dollar,  $. 

280.  The  Silver  Coins  are  the  fifty  cent,  twenty-five  cent, 
twenty  cent,  ten  cent,  and  five  cent  pieces. 

281.  The  Copper  Coin  is  the  cent  piece. 

282.  There  are  no  Canadian  gold  coins.     The  larger  denomi- 
nations consist  of  paper  currency  and  the  gold  coins  of  England 
and  the  United  States. 

ENGLISH  MONEY 

283.  English  or  Sterling  Money  is  the  legal  currency 
of  Great  Britain.     Its  unit  is  the  pound  sterling. 

TABLE  : 

4  farthings  (far.)  =1  penny,  d. 
12  pence  =  1  shilling,  s. 

=        P°und'  £' 


20  shilling 

sovereign,  sov 

284.  The  intrinsic  value  of  the  pound  or  sovereign  in  United 
States  money  is  $4.8665. 

285.  Sterling  coins  are  made  925  parts  pure  gold  or  sil- 
ver and  75  parts  alloy. 

286.  The  Gold  coins  are  the  sovereign  and  half  sovereign. 

287.  The  Silver  coins  are  the  crown  (5s),  half  crown,   shil- 
ling, and  the  six  and  three  penny  pieces. 

288.  The  Copper  coins  are  the  penny,  half  penny,  and  far- 
thing. 

FRENCH  MONEY 

289.  French  Money  is  the  legal  currency  of  France.    The 
unit  is  the  franc. 

TABLE  : 

10  millimes  (m)  =  1  centime,  ct. 
10  centimes  =  1  decime,  dc. 

10  decimes  =  1  franc,  fr. 

290.  The  intrinsic  value  of  the  franc  in  United  States  money 
is  $.193. 


DENOMINATE  NUMBERS  97 

291.  The  Gold  coins  of  France  are  the  100,  40,  20,  10,  and 
5  franc  pieces. 

292.  The  Silver  coins  are  the  5,  2,  and  1  franc,  and  the  50 
and  25  centime  pieces. 

293.  The  Bronze  coins  are  the  10,  5,  2,  and  1  centime  pieces. 

GERMAN  MONEY 

294.  German  Money  is  the  legal  currency  of  the  German 
Empire.     The  unit  is  the  mark. 

TABLE : 

100  pfennigs  —  1  mark. 

295.  The  intrinsic  value  of  the  mark  in  United  States  money 
is  $.2385. 

296.  The  Gold  coins  of  Germany  are  the  20,    10,   and  5 
mark  pieces. 

297.  The  Silver  coins  are  the  2  arid   1   mark  pieces,   and 
the  20  pfennig  piece. 

298.  The  Nickel  coins  are  the  10  and  5  pfennig  pieces. 


Measures  of  Weight 

299.  Weight  is  the  measure  of  the  earth's  gravity. 

300.  The  unit  of  weight  is  the  Troy  pound  as  registered  at 
the  United  States  mint.     It  contains  5760  grains. 

301.  Measures   of   Weight   are   of  four  kinds:     Troy 
Weight,  Avoirdupois  Weight,  Apothecaries'  Weight,  and  Diamond 
Weight. 

TROY  WEIGHT 

302.  Troy  Weight  is  used  in  weighing  gold,   silver,   and 
other  precious  metals  ;  in  philosophical  experiments,  and  is  the 
standard  at  the  United  States  mint. 

TABLE : 

24  grains  (gr.)     =  1  pennyweight,  pwt. 
20  pennyweights  =  1  ounce,  oz. 
12  ounces  =  1  pound,  Ib. 


98  MODERN    BUSINESS    ARITHMETIC 

AVOIRDUPOIS  WEIGHT 

303.  Avoirdupois  Weight  is  used  in  weighing  all  kinds 
of  merchandise,  farm  produce,  and  metals,  except  the  precious 
metals. 

304.  Its  unit  is  the  pound,  which  contains  7000  Troy  grains. 

TABLE : 

16  sixteenths  =  1  ounce,  oz. 

16  ounces  =  1  pound,  Ib. 

100  pounds  =  1  hundredweight,  cwt. 

20  cwt.,  or  2000  Ibs.  =  =  1  ton,  T. 

305.  The  Long  Ton  used  in  estimating  duties  on  imported 
goods,  and  in  weighing  coal  and  iron  at  the  mines,  contains  2240 
avoirdupois  pounds. 

TABLE : 

16  ounces  =  1  pound,  Ib. 

28  pounds  =  1  quarter,  qr. 

4  quarters  =  1  hundredweight,  cwt. 

20  cwt.  or  2240  Ibs.   ==  1  ton,  T. 

OTHER   AVOIRDUPOIS   MEASURES  : 

100  pounds  of  grain  =  1  cental. 

100  pounds  of  fish  =  1  quintal. 

100  pounds  of  nails  =  1  keg. 

196  pounds  of  flour  =  1  barrel. 

200  pounds  of  pork  or  beef  =  1  barrel. 
280  pounds  of  salt  =  1  barrel. 

240  pounds  of  lime  =  1  barrel. 

306.  Gross  Weight   is  the  total  weight,   including  box, 
barrel,  crate  or  other  covering. 

307.  Net  Weight  is  the  gross  weight  less  the  weight  of  the 
box,  barrel,  crate,  or  other  covering. 

308.  In  California  nearly  all  grains,   vegetables,   fruits,   and 
seeds  are  bought  and  sold  by  the  avoirdupois  pound  or  cental. 

'  309.  In  many  States  the  bushel  is  the  standard  of  weight  in 
buying  and  selling  such  commodities,  the  weight  of  a  bushel  de- 
pending upon  the  law  or  custom  of  each  State. 


DENOMINATE  NUMBERS  99 

310.  The  following  table  gives  the  weight  of  a  bushel  in 
California  and  about  the  average  weight  in  other  States : 

OTHER  OTHER 

CAL.   STATES  CAL.   STATES 

Barley  50  Ibs.  48  Ibs.  Flaxseed  56  Ibs.  56  Ibs. 

Beans  60  Ibs.  60  Ibs.  Oats  32  Ibs.  32  Ibs. 

Blue  Grass,  seed  14  Ibs.  14  Ibs.  Onions  50  Ibs.  57  Ibs. 

Buckwheat  40  Ibs.  48  Ibs.  Potatoes  60  Ibs.  60  Ibs. 

Corn,  shelled  52  Ibs.  56  Ibs.  Rye  54  Ibs.  56  Ibs. 

Corn,  ears  68  Ibs.  68  Ibs.  Wheat  60  Ibs.  60  Ibs. 

APOTHECARIES'  WEIGHT 

311.  Apothecaries'    Weight   is   used   by    druggists   in 
weighing  dry  medicines  for  filling  prescriptions.     Most  drugs 
are  bought  at  wholesale  by  avoirdupois  weight. 

312.  Its  Unit  is  the  pound,  containing  5760  troy  grains. 

TABLE : 
20  grains  (gr.xx)    =  1  scruple,  sc.,  or  9. 

3  scruples  (9iij)    =  1  dram,  dr.,  or  3. 

8  drams  (Sviij)     =  1  ounce,  oz.,  or  g. 
12  ounces  (gxij)     =  1  pound,  lb.,  or  tb. 

313.  The  pound,  ounce,   and  grain  are  identical  with  Troy 
weight. 

NOTE — Physicians  usually  write  prescriptions  in  Roman  notation, 
using  small  letters.  Thus,  7  ounces  is  written  5yiJ  (the  final  "i"  being 
written  "  j  "  )  ;  8  drams,  5viiJ  >  12  scruples,  9xij,  etc. 

314.  SIGNS  USED   IN   PRESCRIPTIONS  : 

fy  =  recipe.  P  =  small  part 

aa  =  equal  quantities.  P.  aeq  =  equal  parts. 

ss  =  half  q.  p      =  as  much  as  you  please. 

gr.  =  grain  misce  =  mix. 

DIAMOND  WEIGHT 

315.  Diamond  Weight  is  used  in  weighing  diamonds  and 
other  precious  stones. 

TABLE : 

2  sixty-fourths     =  1  thirty-second  of  a  carat. 
2  thirty-seconds  =  1  sixteenth  of  a  carat. 
2  sixteenths          =  1  eighth  of  a  carat. 
.  ,    ,  _  (  1  fourth  of  a  carat,  or 

"  {  1  carat  grain  =  .792  Troy  grains. 
4  carat  grains       =  1  carat  =  3.168  Troy  grains. 


100  MODERN    BUSINESS    ARITHMETIC 

316.  The  word  carat  is  also  used  to  express  the  proportion 
of  pure  gold  in  a  mixture,  24  carats  representing  pure  gold. 
Thus,  "  18  carats  fine,"  means  that  in  the  mixture  there  are  18 
parts  of  pure  gold  and  6  parts  alloy,  or  base  metal. 


Measures  of  Capacity 

317.  Measures  of  Capacity  are  those  used  in  estimating 
the  contents  of  a  given  space. 

318.  Measures  of  capacity  are  divided  into  two  classes  —  liquid 
measures,  and  dry  measures. 

LIQUID  MEASURE 

319.  Liquid  measure  is  used  in  measuring  liquids    of   all 
kinds. 

TABLE  : 

4  gills  (gi.)  =  1  pint,  pt. 
2  pints  =  1  quart,  qt. 

4  quarts  =  1  gallon,  gal. 
31i  gallons  =  1  barrel,  bbl. 
2  barrels  =  1  hogshead,  hhd. 

NOTE  —  The  term  BARREL  is  applied  to  casks  of  various  sizes  which 
contain  31  1  gallons  or  over.      Under  31  \  gallons  they  are  called  KEGS. 

320.  The  Unit  of  liquid  measure  is  the  gallon^  which  con- 
tains 231  cubic  inches. 

NOTE  —  In  estimating  the  contents  of  cisterns,  reservoirs,  etc.,  7|  gal- 
lons are  allowed  to  each  cubic  foot. 

APOTHECARIES'  FLUID  MEASURE 

321.  Apothecaries'  Fluid  Measure  is  used  by  drug- 
gists in  measuring  liquids  for  filling  prescriptions. 


60  minims  (ffl)    =1  fluid  drachm,  f3« 
8  fluid  drachms  =  1  fluid  ounce,  f£. 
16  fluid  ounces  =  1  pint,  O. 
8  pints  =  1  gallon,  cong. 

NOTE  —  Cong.,  abbreviation  of  the  Latin  CONGIUS,  for  gallon;  O.,  for 
OCTARIUS",  is  Latin  and  means  ONE-EIGHTH. 

NOTE  —  The  MINIM  is  equivalent  to  one  drop  of  water.  The  gallon  is 
the  same  as  in  liquid  measure,  and  contains  231  cubic  inches. 


DENOMINATE  Xr.MBKRS  101 

322.  As  in  Apothecaries'  Weight  the  symbols  are  written  be- 
fore the  numbers  to  which  they  refer.     Thus,   O4  f£7  is  read 
4  pints  7  fluid  ounces. 

DRY  MEASURE 

323.  Dry  Measure  is  used  in  measuring  grain,  fruits,  veg- 
etables, and  other  dry  articles. 

324.  The  Unit  of  dry  measure  is  the  bushel,  which  contains 
2150.42  cubic  inches. 

TABLE : 

2  pints  (pt.)  ==  1  quart,  qt. 
8  quarts  =  1  peck,  pk. 

4  pecks  =  1  bushel,  bu. 

NOTE — In  some  places  the  DRY  GALLON  of  4  quarts  is  used  in  measur- 
ing berries  and  small  fruits.  It  contains  268.8  cubic  inches. 

NOTE — In  estimating  the  contents  of  bins,  boxes,  etc.,  f  of  the  num- 
ber of  cubic  feet  will  give  the  number  of  bushels,  sticken  measure,  and 
|  of  this  number  of  bushels  will  give  the  number  of  heaped  bushels. 


Measures  of  Extension 

325.  Extension  has  one  or  more  of  the  dimensions,  length, 
breadth,  and  thickness.     It  may  be  a  line,  a  surface,  or  a  solid. 

326.  A  I/ine  has  only  one  dimension — length. 


1  inch  2  inches 

4  inches 

NOTE — An  inch  may  be  divided  into  halves,   quarters,    or  eighths,   or 
any  other  fractional  part. 

327.  I^inear  Measure  is  used  in  measuring  lines  and  dis- 
tances.    It  is  also  called  long  measure. 

UNBAR  MEASURE 

TABLE : 

12  inches  (in.)  =  1  foot,  ft.  40  rods  =  1  furlong. 

3  feet  =  1  yard,  yd.  8  furlongs,  or 

5i  yards,  or  \       _         A      A  320  rods,  or         =1  mile. 

16i  feet         j  5280  feet 

328.  The  U.  S.  Standard  Unit  of  extension  is  the  yard  of 
3  feet,  or  36  inches. 


102 


MODERN    BUSINESS    ARITHMETIC 


SURVEYORS'  I/INEAR 

329.  Surveyors'  Linear  Measure  is  used  by  surveyors 
in  measuring  distances  on  land. 

330.  The  Unit  is  the  chain,  the  measure  of  which  is  as  fol- 
lows : 

TABLE : 
7.92  inches  =  1  link,  1. 


1  chain  =  4  rods. 
1  chain  =  22  yards. 
1  chain  =  66  feet. 
1  chain  =100  links. 
1  chain  =  792  inches. 


25  links        =  1  rod,  rd. 
4  rods  —  1  chain,  ch. 

80  chains     '==  1  mile,  mi. 


Therefore,  4  rods  =  22  yards  =  66  feet  =  100  links  =  792 
inches. 

SQUARE  MEASURE 

331.  Square  Measure  is  used  in  computing  the  areas  of 
plane  surfaces. 

332.  Surface  has  two  dimensions,  length  and  breadth. 

333.  Area  is  the  number  of  square  units  in  a  given  surface. 

334.  A   Rectangle    is    a    plane   figure 
bounded  by  four  sides  and  having  four  right 
angles. 

335.  A  Square  is  an  equilateral  (equal 
sides)  rectangle. 

TABLE : 

144  square  inches  ==  1  square  foot,  sq.  ft. 

9  square  feet  =  1  square  yard,  sq.  yd. 

301  square  yards  =  1  square  rod,  sq.  rd. 

160  square  rods  =  1  acre,  A. 

640  acres  =  1  square  mile,  sq.  mi. 

36  square  miles  =  1  township,  Tp. 

336.  The  area  of  a  rectangle  is  found  by 
taking  the  product  of  the  two  dimensions. 

NOTE — In  computing  the  square  units  in  a  given  surface  where  the 
length  and  breadth  are  given,  the  product  of  these  two  dimensions 
equals  the  number  of  square  units  in  a  row  multiplied  by  the  number  of 
rows.  Thus,  instead  of  3  feet,  the  width,  times  5  feet,  the  length,  the 
analysis  is  3  times  the  five  square"  feet  in  a  row,  or  15  square  feet. 


DENOMINATE  NUMBERS 


103 


SURVEYORS'  SQUARE  MEASURE 

337.  Surveyors'  Square  Measure  is  used  in  computing 

the  area  of  land. 

338.  The  Unit  of  land  measure  is  the  acre. 

TABLE  : 
=  1  square  rod,  sq.  rd. 

=  1  Square  cham'  Sq-  ch" 


625  square  links 
16  square  rods    jr 
10000  square  links 
10  square  chains, 
160  square  rods 
640  acres 
36  square  miles 


. 

=  1  square  mile. 
=  1  township,  Tp. 

339.  A  Principal  Meridian  is  an  imaginary  line  extend- 
ing north  and  south,  from  which  government  surveys  are  made. 

340.  A  Base  Isine  is  an  imaginary  line  extending  east  and 
west,  crossing  the  meridian  at  a  fixed  point. 

DIAGRAM  : 


T4N 
R4W 

- 

I 

z 
< 

Q 

T3N 
R1E 

T3N 
R4E 

T2N 
R2W 

K 
u 

5 

• 

BASE 

LINE 

Tl  S 
R3  E 

T2  S 
R  4W 

CIPAL 

Z 
E 

0. 

T4  S 
R3W 

T4  S 
R2E 

341.  Townships  are  located  north  and  south  of  the  Base  Line 
by  numbers,  and  east  and  west  of  the  Principal  Meridian  by  the 
number  of  the  range  or  row. 


104 


MODERN    BUSINESS    ARITHMETIC 


NOTE — The  foregoing  are  read  :  Township  4  North,  Range  4  West ; 
Township  3  North,  Range  1  East ;  Township  2  North,  Range  2  West ; 
etc. 

342.  In  Regular  Surveys,  townships  are  six  miles  square 
and  contain  36  square  miles.     Irregular  townships  contain  dif- 
ferent areas. 

343.  Regular    Townships    are  divided    into    sections  or 
square  miles  which  are  numbered  as  follows  : 

DIAGRAM    OF   A    TOWNSHIP  : 
NORTH 


6 

5 

4 

3 

2 

1 

7 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

19 

20 

21 

22 

23 

24 

30 

29 

28 

27 

26 

25 

31 

32 

33 

34 

35 

36 

DIAGRAM   OF   A   SECTION  : 


NE  i 

160  A 

W| 

320  A 

NW  i 

of  SEi 

40  A 

E  i  of 

SE  \ 

80  A 

SOUTH 

344.  A  Section  is  one  mile 
square  and  contains  640  acres. 
Sections  may  be  subdivided  into 
halves  and  quarters ;  quarters 
into  quarter-quarters,  etc. 

In  cities  and  towns,  land  is 
described  by  giving  the  number 
of  the  lot,  the  number  of  the 
block,  and  the  addition,  or  the 
original  plat  of  the  city  as  re- 
corded on  the  official  survey. 


— The  40  acre  portion  of  the  above  diagram  would  be  read,  "the 
northwest  quarter,  of  the  southeast  quarter,  of  section  No.  16. 


DENOMINATE  NUMBERS 


105 


CUBIC  MEASURE 

345.  Cubic  Measure  is  used   in 
X      measuring  the  contents  of  solids. 

346.  A  Rectangular  Solid  is  one 

bounded  by  six  rectangular  surfaces. 

347.  A  Cube  is  a  rectangular  solid  whose 
surfaces  are  equal  squares. 

348.  The  Volume,  or  solid  contents,  are 
found  by  taking  the  product  of  the  three  di- 
mensions. 


TABLE : 

1728  cubic  inches  =  1  cubic  foot,  cu.  ft. 
27  cubic  feet  =  1  cubic  yard,  cu.  yd. 

1  cubic  yard  =  1  load. 

349.     Wood  Measure  is  used  in  measuring  wood. 


TABLE : 

16  cubic  feet       =  1  cord  foot. 
8  cord  feet  or 
128  cubic  feet 


=  1  cord. 


350.     Rough  stone  is  sometimes  reckoned  by  the  perch',  which 
contains  24 J  cubic  feet. 


Time  Measure 


351. 


Time  is  a  measured  portion  of  duration. 

352.  The  revolution  of  the  earth  upon  its  axis  causes  day 
and  night.     Its  revolution  around  the  sun  requires  one  year  of 
365  days  5  hours  48  minutes  49.7  seconds. 

353.  In  reckoning  time,  365  days  are  called  a  common  year. 
This  being  almost  one-fourth  of  a  day  less  than  the  exact  year, 

every  fourth  year  is  given  one  more  day,  and  is  called  leap  year. 
As  this  method  is  not  absolutely  accurate,  the  centennial  years 
are  not  leap  years  unless  divisible  by  400. 


106 


MODERN    BUSINESS    ARITHMETIC 


354.  The  Unit  of  time  measure  is  the  day  of  24  hours. 

TABLE : 

60  seconds  =  1  minute,  min. 

60  minutes  =  1  hour,  hr. 

24  hours  =  1  day,  da. 

7  days  =  1  week,  wk. 

4  weeks  =  1  lunar  month,  lu.  mo. 

365  days  —  1  common  year. 

366  days  ==  1  leap  year. 
12  months  =  1  year,  yr. 

100  years        =  1  century,  C. 

355.  The  Months  and  Seasons  of  the  year  are  as  follows: 


MONTH 


ABBREVIATED 


SEASON 

WINTER 

SPRING 

SUMMER 

AUTUMN 

WINTER 

356.  The  number  of  days  in  each  month  may  be  kept  in 
mind  by  memorizing  the  following  rhyme  : 

"Thirty  days  hath  September, 

April,  June,  and  November  ; 
All  the  rest  have  thirty-one, 

Save  February,  which  alone 
Hath  twenty-eight,  and  one  day  more 

We  add  to  it  one  year  in  four." 

NOTE — In  business  computations,  30  days  are  usually  called  a  month. 
In  reckoning  time,  the  prevailing  custom  is  to  count  years  and  months 
by  dates  only,  and  the  extra  days  as  days.  Thus,  from  February  10th 
to  March  31st,  the  time  is  1  month  (  from  February  10th  to  March  10th  ) 
and  21  days  (from  March  10th  to  March  31st),  instead  of  49  days,  or  1 
month  and  19  days. 


January 
February 
February  (leap  yr,  ) 

Jan. 
Feb. 

March 
April 
May 

Mar. 
Apr. 
May 

June 
July 
August 

June 
July 
Aug. 

September 
October 
November 

Sept. 
Oct. 
Nov. 

December 

Dec. 

DENOMINATE  NUMBERS  107 

Circular  Measure 

357.  Circular  or  Angular  Measure  is  used  in  measur- 
ing angles,  arcs,  directions,  elevations,  etc. 

358.  The  Unit  is  the  degree,  the  ^fa  part  of  the  circumfer- 
ence of  a  circle. 

359.  A  Circle  is  a  plane  figure  bounded  by  a  curved  line, 
every  point  of  which  is  the  same  distance  from  its  center. 

360.  The  Circumference  of  a  circle  is 
the  line  that  bounds  it. 

361.  An  Arc  is  a  part  of  a  circle. 

362.  An  Angle  is  the  divergence  of  two 
lines  from  a  common  point. 

363.  A  Right  Angle  is  formed  by  lines 
drawn  perpendicular  to   each   other   from   a 
common  point. 

364.  A  circle  may   be  divided    into    360 
degrees.     A  semi-circle  into  180  degrees.     A 
quadrant  into  90  degrees,  etc. 

365.  A  Diameter  of  a  circle  is  a  line 
passing  through  the  center  and  terminating  in 
its  circumference. 

366.  A  Radius  is  one-half  a  diameter. 

367.  To  measure  an  arc  is  to  ascertain  the  number  of  degrees 
between  the  radii  joined  by  the  arc. 

TABLE : 

60  seconds  (  "  )  =  1  minute,  (  '  ) 
60  minutes  =  1  degree,  (  °  ) 
30  degrees  =  1  sign,  (  s.  ) 

12  signs  )  '  1  .  .  /  c  x 
360  degrees  \ 

368.  One  degree  on  a  meridian  or  on  the  equator  is  equal  to 
about  69.16  common  or  statute  miles. 


108  MODERN    BUSINESS    ARITHMETIC 

COUNTING  TABLE :  PAPER   TABLE : 

12  units   =  1  dozen,  doz.  24  sheets   =  1  quire,  qr. 

12  dozen  ==1  gross,  gro.  20  quires  —  1  ream,  rni. 

12  gross   =  1  great  gross,  G.  gro.  2  reams     —  1  bundle,  bdl. 

20  units   =  1  score.  5  bundles  =  1  bale. 

BOOKS : 

A  sheet  folded  into    2  leaves  is  called  a  folio. 
A  sheet  folded  into    4  leaves  is  called  a  quarto. 
A  sheet  folded  into    8  leaves  is  called  an  octavo. 
A  sheet  folded  into  12  leaves  is  called  a  12  mo. 
A  sheet  folded  into  16  leaves  is  called  a  16  mo. 


Comparison  of  Weights 

369.  The  Unit  of  Troy  weight  and  of  Apothecaries'  weight 
is  the  pound  which  contains  5760  grains. 

370.  The  Unit  of  Avoirdupois  weight  is  the  pound  which 
contains  7000  grains. 

371.  The  Troy  ounce  and  the  Apothecaries'  ounce  each  con- 
tain i^  of  5760  grains  =  480  grains. 

372.  The  Avoirdupois  ounce  contains  TV  of  7000  grains  = 
437^  grains. 

COMPARATIVE  TABLE: 

1  pound  Troy  or  Apothecaries'  weight  =5760  grains. 

1  pound  Avoirdupois  weight  =  7000  grains. 

(Avoirdupois  the  greater  by  1240  grains). 

1  ounce  Troy  or  Apothecaries'  weight  =  480  grains. 
1  ounce  Avoirdupois  weight  =  437^  grains. 

(Troy  and  Apothecaries'  the  greater  by  42|  grains.) 

373.  In  changing  from  one  kind  of  weight  to  another,   the 
quantities  must  first  be  reduced  to  grains. 


Reduction  of  Denominate  Numbers 

374.  Reduction  of  Denominate  Numbers  is  the  pro- 
cess  of   changing  their    denominations  without    altering   their 
values. 

375.  Reduction  Ascending  is  to  reduce  the  given  num- 
ber to  a  higher  denomination.     Thus,  36  pence  reduced  to  shil- 
lings =  3  shillings. 

376.  Reduction  Descending  is  to  reduce  the  given  num- 
ber to  a  lower  denomination.     Thus,    £4   reduced  to    shillings 
=  80  shillings. 

377.  To   reduce   to  a  higher  denomination,   divide  by  the 
number  of  units  required  to  make  the  higher  denomination. 

378.  To  reduce  to  a  lower  denomination,   multiply  by  the 
number  of  units  of  the  lower  denomination  required  to  make  one 
the  higher. 

379.  Reduction  Ascending. 

EXAMPLE  :     Reduce  1250  farthings  to  £. 

4  farthings  =  1  penny     4  )  1  2  5  0  far. 
12  d.  =  1  s.  12  )  3  1  2  d.  and  2  far.  remainder. 

20  s.  =  £l.  20  )  26  s.  and  0  d.  remainder. 

£l       and  6  s.  remainder. 
Answer,  £l  6s.   Od.   2  far. 

380.  Reduction  Descending. 

EXAMPLE  :     Reduce  £3  7s.  3  d.  to  farthings. 

20s.  =  £l.  804  d. 

3  , 3  d.  added. 

60  s.  807  d. 

_]_  s.  added  4  far.  =  1  d. 

67  s.  1628  far.,  Answer. 

12  d.  =  1  s. 
804  d. 


110  MODERN    BUSINESS    ARITHMETIC 

ENGLISH  MONEY 

381.  Solve  the  following  : 

1.  Reduce  £4  5s.  7d.  to  pence. 

2.  Reduce  £l4  10s.  9d.  2  far.  to  farthings. 

3.  Reduce  721  pence  to  higher  denominations. 

4.  Reduce  £47  lid.  to  farthings. 

5.  Reduce  37425  far.  to  higher  denominations. 

6.  In  %2  of  a£  how  many  pence  ? 

7.  In  .725  of  a  ;£  how  many  farthings? 

8.  Reduce  845.75  pence  to  £  s.  d.  and  far. 

9.  A  traveler  from  England  lands  in  New  York  with  /50 
10s.  6d.  which  he  exchanges  for  U.  S.  money  at  intrinsic  value. 
How  much  does  he  receive  ? 

10.     An  American  traveling  in  England  has  $8273.05  changed 
to  English  money.     How  much  did  he  receive  ? 

FRENCH  AND  GERMAN  MONEY 

382.  Solve  the  following  : 

1.  How  many  francs  in  3240  centimes  ? 

2.  Reduce  42  francs  to  centimes. 

3.  How  many  dollars  U.  S.  money  in  2123  francs? 

4.  How  many  francs  in  $2123  U.  S.  money? 

5.  An  Englishman  lands  in  France  with  ^200  and  exchanges 
it  for  French  money.     How  much  should  he  receive  on  the  in- 
trinsic basis  ? 

6.  How  many  marks  in  4280  pfennigs  ? 

7.  Reduce  75  marks  to  pfennigs. 

8.'    How  many  dollars  U.  S.  money  in  260.5  marks? 
9.     How  many  marks  in  $2623.50  U.  S.  money  ? 
10.     A  Frenchman  traveling  in  Germany  desired  to  change  his 
477  francs  for  marks.     How  many  should  he  receive  ? 

TROY  WEIGHT 

383.  Solve  the  following  : 

1.  .  Reduce  5  Ibs.  7  oz.  to  pennyweights. 


DENOMINATE  NUMBERS  111 

2.  Reduce  3  Ibs.  4  oz.  15  pwt.  10  gr.  to  grains. 

3.  Reduce  17  Ibs.  18  pwt.  22  gr.  to  gr. 

4.  Reduce  5760  gr.  to  ounces. 

5.  Reduce  8880  pwt.  to  Ibs. 

6.  Reduce  35179  gr.  to  higher  denominations. 

7.  What  will  be  the  cost  of  a  gold  medal  weighing  11  pwt. 
16  gr.  at  5  cents  per  grain  ? 

8.  How  many  spoons  weighing  1%  oz.  each  can  be  made 
from  a  bar  weighing  5  Ibs.  10  oz.  1 

9.  A  miner  wishing  to  have  a  watch  case  made,   sent  to  the 
watchmaker  2  oz.  8  pwt.  9  gr.  of  gold  9Ao  pure.     If  the  watch- 
maker charged  $17.50  for  his  labor,  and  $22.50  for  the  works, 
what  was  the  total  value  of  the  watch  ? 

10.     What  is  5  Ibs.  10  oz.  15  pwt.  12  gr.  of  gold  dust  worth, 
at  84  cents  a  pwt.  ? 

AVOIRDUPOIS  WEIGHT 
384.     Solve  the  following  : 

1.  Reduce  5  cwt.  75  Ibs.  12  oz.  to  ounces. 

2.  Reduce  2  T.  16  cwt.  48  Ibs.  to  pounds. 

3.  Reduce  2560  oz.  to  hundredweights. 

4.  Reduce  587650  oz.  to  higher  denominations. 

5.  Reduce  29120  Ibs.  to  long  tons. 

6.  An  importer  received  a  shipload  of  540  long  tons  of  coal 
costing  $3  per  ton,  freight  25  cents  per  ton,  and  duty  75  cents 
per  ton.     If  he  sell  it  at  $5  per  standard  ton,  what  will  be  his 
gain? 

7.  What  will  be  the  cost  of  7  carloads  of  wheat,   each  car 
containing  20  tons,  at  $1.15  per  cental? 

8.  In  building  a  house,  I  used  2  kegs  of  six  penny  nails  at 
3%  cents  per  pound,  5  kegs  of  8's  at  3V2  cents  per  pound,   7l/2 
kegs  of  spikes  at  31/4  cents  per  pound,   and  ll/2  kegs  of  shingle 
nails  at  4  cents  per  pound.     What  was  the  total  cost  of   the 
nails  ? 

9.  What  is  the  capacity  of  the  smallest  car  that  will  exactly 
carry  either  barley,  flaxseed,  wheat,  or  oats,  whole  bushels,  Cali- 


112    .  MODERN    BUSINESS    ARITHMETIC 

fornia  weights;  and  how  many  bushels  of  each  kind  would  be  re- 
quired for  a  load  ? 

10.  Find  the  total  cost  of  the  barley,  flaxseed,  wheat,  and 
oats  in  the  above,  if  the  cost  of  the  flaxseed  was  Vs  more  than 
the  wheat,  the  cost  of  the  wheat  1A  more  than  the  barley,  the 
cost  of  the  barley  Vs  more  than  the  oats,  and  the  oats  was  worth 
30  cents  per  bushel. 

APOTHECARIES'  WEIGHT 

385.  Solve  the  following  : 

1.  Reduce  3  Ibs  58  35  to  drams. 

2.  Reduce  1  Ib.  57  33  92  gr.15  to  grains. 

3.  Reduce  4245  grains  to  higher  denominations. 

4.  Reduce  12560  scruples  to  pounds. 

5.  How  many  2 -grain  capsules  can  be  made  from   Si  3l  9l 
of  quinine.? 

6.  A  druggist  made  4200  four-grain  capsules  of  a  certain  kind 
of  medicine.     Allowing  one  grain  for  the  weight  of  each  shell, 
what  was  the  total  weight  ? 

7.  If  the  above  medicine  cost  $1  an  ounce,   and  retailed  for 
25  cents  per  dozen  capsules,  what  would  be  the  gain  ? 

8.  Medicine  bought  for  $12  a  pound,  Apothecaries'  weight, 
is  sold  for  10  cents  a  scruple.     What  would  be  the  gain  on  11 
pounds  ? 

9.  An  ounce  of  medicine  will  make  how  many  doses,  if  each 
dose  requires  Vw  of  a  grain? 

10.  How  many  3-grain  pills  can  be  made  from  2  Ibs.  52  32 
92  gr.2  of  drugs,  and  what  will  be  the  cost  at  15  cents  a 
dozen  ?  

Comparison  of  Weights 

386.  Solve  the  following  : 

1.  Reduce  10  Ibs.  Troy  to  Avoirdupois  pounds. 

2.  Reduce  10  Ibs.  Avoirdupois  to  Troy  pounds. 

3.  Reduce  10  Ibs.  Avoirdupois  to  Apothecaries'  weight. 


DENOMINATE  NUMBERS  113 

4.  Reduce  10  Ibs.  10  oz.  10  pwt.  10  gr.  Troy  to  Apothecaries' 
weight. 

5.  Reduce  17  Ibs.  12  oz.  Avoirdupois  to  Troy  weight. 

6.  Which  is  the  heavier  and  how  much,  a  pound  of  gold  or  a 
pound  of  feathers  ? 

7.  Which  is  the  heavier,   an  ounce  of  gold  or  an  ounce  of 
feathers,  and  how  much  ? 

8.  A  man  bought  a  bar  of  silver  weighing  125  pounds,  Avoir- 
dupois weight,  for  60  cents  an  ounce,  and  sold  it  for  60  cents  an 
ounce,  Troy  weight.     Did  he  gain  or  lose,  and  how  much  ? 

9.  A  druggist  bought  5  pounds  of  quinine  at  $12  per  pound, 
avoirdupois  weight,  and  sold  it  in  2-grain  capsules  at  10  cents 
per  dozen.     What  was  his  profit  ? 

10.  A  grocer  uses  an  Apothecaries'  scales  in  selling  bicarbon- 
ate of  soda.  Out  of  how  much  does  he  cheat  his  customers  in 
selling  a  48-pound  box,  the  selling  price  being  45  cents  per 
pound? 


LIQUID  MEASURE 

387.     Solve  the  following  : 

1.  Reduce  5  gal.  3  qts.  1  pt.  to  pints. 

2.  Reduce  3  bbls.  22  gal.  2  qts.  1  gi.  to  gills. 

3.  Reduce  4  hhds.  28  gal.  1  pt.  to  gills. 

4.  Reduce  2268  pts.  to  barrels. 

5.  Reduce  14271  gills  to  higher  denominations. 

6.  How  many  barrels  in  a  tank  that  will  hold   1055   gallons 
1  quart? 

7.  How  many  1^  pint  bottles  can  be  filled  from  a  cask  of 
wine  containing  45  gallons  ? 

8.  How  many  pint,  quart,  and  half -gallon  bottles  of  each  an 
equal  number  can  be  filled  from  a  cask  holding  42  gallons  ? 

9.  A  grocer  bought  5  bbls.  of  vinegar  at  $6  a  barrel  and  sold 
it  at  10  cents  a  quart.     What  was  his  gain  ? 

10.  A  grocer's  gal.  measure  was  1  gi.  short  of  correct  measure. 
How  much  would  he  profit  in  selling  a  45  gallon  cask  of  molas- 
ses at  62  cents  per  gallon  by  using  the  short  measure  ? 


114  MODERN    BUSINESS    ARITHMETIC 

APOTHECARIES'  FI/UID  MEASURE 

388.  Solve  the  following  : 

1.  Reduce  cong.7  O5  fSl2  to  fluid  drachms. 

2.  Reduce  O3  fS6  f57  11145  to  minims. 

3.  Reduce  cong.18  fS7  0135  to  minims. 

4.  Reduce  U143456  to  higher  denominations. 

5.  Reduce  £516382  to  higher  denominations. 

6.  How  many  ounce  bottles  can  be  filled  from  a  tankard  con- 
taining cong.ll ? 

7.  A  druggist  fills  124  doz.  fS2  bottles  with  perfume.     What 
quantity  was  required  ? 

8.  Brown  bought  3  gills  of  a  tincture  at  25  cents  per  gill  and 
sold  it  at  15  cents  a  fluid  drachm.     What  did  he  gain  ? 

9.  By  buying  alcohol  at  $4  per  gallon,  liquid  measure,    and 
selling  it  at  10  cents  a  fluid  ounce,  what  would  be  the  gain  on 
five  gallons  ? 

10.  A  druggist  had  3  ounce,  5  ounce,  and  8  ounce  bottles, 
and  wished  to  use  twice  as  many  of  the  3  ounce  as  of  the  5 
ounce,  and  twice  as  many  of  the  5  ounce  as  of  the  8  ounce. 
How  many  bottles  would  be  required  to  hold  the  contents  of  4 
barrels  each  containing  33f  gallons  ? 

DRY  MEASURE 

389.  Solve  the  following  : 

1.  Reduce  5  bu.  3  pk.  5  qt.  to  quarts. 

2.  Reduce  17  bu.  1  pk.  3  qt.  1  pt.  to  pints. 

3.  Reduce  17  bu.  7  qt.  to  pints. 

4.  Reduce  128  pints  to  bushels. 

5.  Reduce  57631  pt.  to  higher  denominations. 

6.  What  will  4  bu.  2  pk.  of  nuts  cost  at  8  cents  per  quart  ? 

7.  Cranberries  bought  for  $5  per  barrel  of  2^  bushels  are 
sold  at  10  cents  per  quart.     What  is  the  gain  on  a  barrel  ? 

8.  If  one  horse  requires  12  quarts  of  oats  per  day,  how  many 
bushels  will  it  take  to  feed  6  horses  8  days  ? 


DENOMINATE  NUMBERS  115 

9.  A  grain  dealer's  bushel  measure  is  too  small  by  1  pint. 
What  does  he  make  dishonestly  in  selling  12  tons  of  wheat  at 
90  cents  a  bushel  ? 

10.  A  dealer  bought  2  bu.  6  qt.  of  berries  at  40  cents  a  pk., 
dry  measure,  and  sold  them  at  10  cents  per  qt.,  liquid  measure. 
What  did  he  gain  ? 

IVINEAR  MEASURE 

390.  Solve  the  following  : 

1.  Reduce  8  rd.  5  yd.  2  ft.  7  in.  to  inches. 

2.  Reduce  1  mi.  4  ch.  2  rd  20  1.  to  inches. 

3.  Reduce  4  leagues  2  mi.  7  fur.  4  yd.  1  ft.  to  inches. 

4.  Reduce  71364  inches  to  higher  denominations. 

5.  Reduce  35824  links  to  higher  denominations. 

6.  If  it  costs  $16000  per  mile  to  build  a  railway,  what  will  be 
the  cost  to  build  5  fur.  23  rd.  5  yd.  1  ft.  6  in.  ? 

7.  How  many  linear  feet  of  boards  will  it  take  to  fence  a 
field  25  rods  wide  by  40  rods  long,  the  fence  to  be  five  boards 
high? 

8.  If  a  steamer  travels  20  miles  an  hour,  how  far  will  she  go 
in  5  days  10  hours  and  30  minutes  ? 

9.  What  will  it  cost  to  fence  a  field  140  rods  long,   80  rods 
wide,  at  $.37l/2  per  rod  for  posts,  and  3  cents  per  linear  foot  for 
the  wire  fencing  ? 

10.  An  automobile  wheel  is  100  inches  in  circumference. 
How  many  times  will  it  revolve  in  going  from  San  Francisco  to 
Los  Angeles,  a  distance  of  484  miles  ? 

SQUARE  MEASURE 

391.  Solve  the  following  : 

1.  Reduce  5  sq.  yd.  4sq.  ft.  72  sq.  in.  to  square  inches. 

2.  Reduce  12  A.  48  sq.  rd.  21  sq.  yd.  to  square  yards. 

3.  Reduce  2  A.  64  sq.  rd.  140  sq.  ft.  to  square  feet. 

4.  Reduce  14285  sq.  in.  to  higher  denominations. 


116  MODERN    BUSINESS    ARITHMETIC 

5.  Reduce  7235  sq.  rd.  to  acres. 

6.  What  will  it  cost  to  lay  a  walk  8  feet  wide  around  the 
outside  of  a  block  300  feet  square,  at  16%  cents  per  square  foot  ? 

7.  Find  the  cost  of  flooring  a  room  at  5  cents  per  square  foot, 
the  distance  around  it  being  280   feet,    and  the  width  %  the 
length. 

8.  What  will  be  the  cost  of  plastering  the  walls  and  ceiling 
of  a  room  40  feet  wide  by  60  feet  long  and  16  feet  high  at  331/ij 
cents  a  square  yard,  allowing  for  a  4-foot  wainscoting,   but  no 
allowance  to  be  made  for  doors  or  windows  ?  • 

9.  A  city  lot  containing  VB  of  an  acre  is  sold  at  $100  per  front 
foot.     If  the  lot  is  90  feet  deep,  what  is  the  total  selling  price? 

10.  Find  the  cost  of  carpeting  a  lodge  room  the  floor  of  which 
is  36  feet  wide,  and  54  feet  long ;  the  carpet  to  be  regular  27  in. 
tapestry  $1.55  per  linear  yard ;  strips  to  run  lengthwise  the  hall, 
and  9  inches  allowed  on  each  strip  for  matching. 

SURVEYORS'  SQUARE  MEASURE 

392.     Solve  the  following  : 

1 .  How  many  acres  in  4  sections  ? 

2.  Reduce  640  sq.  ch.  to  acres. 

3.  Reduce  2  A.  5  sq.  ch.  12  sq.  rd.  to  square  links. 

4.  Reduce  17342  sq.  1.  to  higher  denominations. 

5.  Reduce  5760  sq.  rd.  to  square  chains. 

6.  How  many  acres  in  a  field  23^6  chains  wide,   and  27l/2 
chains  long  ? 

7.  Hill  owns  the  S.  E.  x/4  of  the  N.  W.  %  of  a  section  of  land. 
How  many  acres  has  he  ? 

8.  The  E.  %  of  the  S.  W.  *4  of  a  section  of  land  was  bought 
for  $75  per  acre  and  sold  at  $110  per  acre.     How  much  was 
gained  ? 

9.  A  sold  the  N.  V2  of  the  S.  W.  %  and  the  S.  ¥2  of  the  N.  W. 
X  of  a  section  of  land  at  $62.50  per  acre.     How  much  did  he 
get  for  his  land  ?     Draw  diagram  and  locate  the  property. 


DENOMINATE  NUMBERS  117 

10.  What  is  the  cost  of  a  farm  bought  at  $125  an  acre  and  des- 
cribed as  follows  :  The  E.  Y*  of  the  N.  W.  #  of  the  S.  E.  #  of 
the  N.  E.  #  of  the  S.  W.  Y±  of  section  16,  Tp.  2  N.  Range  3  W.  ? 
Draw  diagram  of  section  16,  and  locate  the  farm. 

CUBIC  MEASURE 
393.     Solve  the  following  : 

1.  Reduce  17  cu.  ft.  132  cu.  in.  to  cubic  inches. 

2.  Reduce  25  cu.  yd.  22  cu.  ft.  to  cubic  feet. 

3.  Reduce  12  cords  to  cubic  feet. 

4.  -Reduce  51840  cu.  in.  to  cubic  feet. 

5.  Reduce  18  cd.  ft.  to  cubic  inches. 

6.  What  will  it  cost  to  dig  a  cellar  16  feet  wide  by  24  feet 
long  and  9  feet  deep  at  60  cents  a  cubic  yard  ? 

7.  How  many  cords  in  a  pile  of  wood  48  feet  long,   6  feet 
high,  and  4  feet  wide  ? 

8.  What  will  be  the  cost  of  building  a  wall  132  feet  long,   4 
feet  6  inches  high,  and  18  inches  wide,  at  $2.40  a  perch  ? 

9.  Allowing  7  bricks    to  the  square  foot    for  ^ach   tier   of 
bricks,  how  many  bricks  will  it  take  to  build  the  sides  and  one 
end  of  a  store  building  27  feet  wide,  120  feet  long,  the  walls  be- 
ing 22  feet  high,  no  allowances  for  openings  or  corners,  and  the 
walls  three  bricks  thick  ? 

10.  A  railway  tunnel  is  ^  of  a  mile  long,  20  feet  wide,  and  18 
feet  high.  If  it  cost  $1.40  per  cubic  yard  to  excavate  it,  $2.75 
per  linear  yard  to  timber  it,  and  $28  per  rod  to  lay  the  track ; 
what  was  the  total  cost  when  finished  ? 

TIME  MEASURE 
394.     Solve  the  following  : 

1.  Reduce  12  yrs.  7  mos.  15  ds.  to  days. 

2.  Reduce  7  wks.  1  da.  12  hrs.  20  min.  to  minutes. 

3.  Reduce  1620  hours  to  higher  denominations. 

4.  Reduce  1342782  seconds  to  higher  denominations. 

5.  How  many  minutes  in  February,  1908  ? 

6.  How  many  more  seconds  in  July  than  in  June? 


118  MODERN    BUSINESS    ARITHMETIC 

7.  Find  the  exact  time  from  March  15th  to  August  23d. 

8.  How  many  times  will  a  clock  that  ticks  3  times  in  every  2 
seconds  tick  in  a  day  ? 

9.  A  note  given  September  15,   1907,   is  due  April  2,   1910, 
How  long  has  it  to  run  ?     Give  answer  in  years,   months,   and 
days. 

10.  A  note  dated  July  1,  1907,  is  written,  "one  year  after 
date  I  promise  to  pay,  etc."  If  this  note  is  discounted  at  bank 
December  21,  1907,  what  is  the  term  of  discount? 

CIRCULAR  MEASURE 
395.     Solve  the  following  : 

1.  Reduce  7°  24'  30"  to  seconds. 

2.  Reduce  45°  50'  54"  to  seconds. 

3.  Reduce  21485'  to  higher  denominations. 

4.  Rednce  457864"  to  higher  denominations. 

5.  Reduce  145°  to  statute  miles. 

6.  New  York  is  74°  3'  west  of  Greenwich.     How  many  sec- 
onds are  they  apart. 

7.  San  Francisco  is  122°  26'  45"  west  of  Greenwich.     How 
many  geographic  miles  is  San  Francisco  from  New  York  ? 

8.  A  dial  of  a  clock  represents  a  circle.     How  many  degrees 
from  12  M.  to  8  p.  M.  ? 

9.  How  many  statute  miles  around  the  earth  on  its  greatest 
circle  ? 

10.  The  earth  revolves  on  its  axis  once  every  24  hours.  How 
many  degrees,  minutes,  and  seconds  will  it  revolve  in  4  hours 
24  minutes  30  seconds? 


396.     Solve  the  following  : 

1  .     What  will  be  the  cost  of  a  great  gross  of  lead  pencils  at 
30  cents  per  dozen  ? 

2.     Brown  sold  5  gross  of  penholders  at  5  cents  each.     What 
did  they  bring  ? 


DENOMINATE  NUMBERS  119 

3.  In  a  crate  containing  f\  of  a  G.  gro.  of  eggs,  1  out  of  every 
18  was  broken ;  the  remainder  were  sold  at  25  cents  per  dozen. 
What  did  they  bring  ? 

4.  A  is  2  score  years  of  age  ;  B  is  as  old  as  A  and  C,   and  C 
is  \  the  age  of  A.     What  is  the  age  of  each  ? 

5.  John  is  12  years  old ;  James  is  as  old  as  John,   plus  -J-  of 
Henry's  age,  and  Henry  is  as  old  as  John  and  James  together. 
Find  the  age  of  James  and  Henry. 

6.  How  many  sheets  of  paper  in  2  reams  ? 

7.  What  will  15  reams  of  20#  14x17  Queen  Bee  flat  paper 
cost  at  9  cents  per  Ib.  ? 

8.  Bought  2  bundles  of  16#    folio  linen  typing  paper  (500 
sheets  17  x  22)  at  12  cents  per  Ib.,  and  after  cutting  the  same  into 
letter  size  (fourths),  sold  it  at  60  cents  per   500  sheets.     What 
was  my  gain  ? 

9.  How  many  sheets  of  paper  28x42  will  it  take  to  print  1000 
16  mo.  books  of  320  pages  each? 

10.  Ten  reams  of  paper  will  make  how  many  octavo  booklets, 
reckoning  500  sheets  to  the  ream  ;  and  how  many  pages  in  each 
allowing  one  sheet  to  each  booklet  ? 


HOME  WORK— No.  13 

1.  Which  has  the  greater  intrinsic  value,  ^20,  400  marks,  or 
500  francs,  and  by  how  much  in  U.  S.  money? 

2.  Which  is  the  heavier,   a  10-pound  steel  sledge,   or  a  10- 
pound  sack  of  silver,  and  how  much  ? 

3.  Which  is  the  heavier,  a  4-ounce  gold  watch  case  or  a  4- 
ounce  boxing  glove,  and  how  much  ? 

4.  How  many  10-grain  powders  can  be  made  from  Ibl,  Svij, 
5iv,  9ij  of  drugs  ? 

5.  How  many  pint,  quart,  and  two-quart  bottles,  of  each  an 
equal  number,  can  be  rilled  from  a  keg  containing  10  gal.   2  qts. 
of  cider  ? 


120  MODERN    BUSINESS    ARITHMETIC 

6.  A  farm  is  60  chains  long  and  124  rods  wide.     How  many 
acres  does  it  contain  ? 

7.  Draw  a  map  and  locate  Tp.  2  N.  and  R.  3  E.,   also  locate 
the  N.  %  of  the  S.  W.  X  of  the  N.  E.  X  of  Section  21.     How 
many  acres  ? 

8.  How  many  perches  of  stone  in  a  wall  66  ft.   long,    15   ft. 
high,  and  2  ft.  6  in.  thick? 

9.  How  many  more  seconds  in  January  than   in  February 
1908? 

10.  A  grocer's  scales  is  /^  oz.  short  in  every  pound.  Out  of 
how  much  does  he  cheat  his  customers  in  selling  a  310-pound 
barrel  of  sugar  worth  6  cents  per  pound  ? 


Longitude  and  Time 

397.  A  Meridian  is  any  imaginary  line  extending  from 
pole  to  pole  on  the  earth's  surface. 

398.  There  are  three  First  Meridians  : 

1.  The  Meridian  of  Greenwich  —  the  one    passing 
through  Greenwich,  a  suburb  of  L,ondon,  England. 

2.  The  Meridian   of    Washington,  D.    C. — the  one 
passing  through  the  observatory  at  Washington. 

3 .  The  Meridian  of  Paris — the  one  passing  through 
Paris,  France. 

399.  Longitude  is  the  distance  east    or    west  of  a  first 
meridian. 

400.  Using  the  Meridian  of  Greenwich  as  the  first  mer- 
idian, Washington  is  77°  0'  15"  west  longitude,   and  Paris  is   2° 
20'  east  longitude. 

401.  Standard   Time  in  the  United  States,  for  conven- 
ience, has  been  established  as  follows  : 

1.  Eastern  time,  taken  when  the  sun  is  on  the  meridian  75° 
west  of  Greenwich. 

2.  Central  time,  taken  when  the  sun  reaches  the  meridian  of 
90°  west. 

3.  Mountain  time,  taken  when  the  sun  reaches  the  meridian 
of  105°  west. 

4.  Pacific  time,  taken  when  the  sun  reaches  the  meridian  of 
120°  west. 

402.  It  will  be  noticed  that  the  difference  of  longitude  of  the 
above  is  15°  each.     The  difference  of  time  is  one  hour,  the  same 
time  being  used  in  all  territory  of  7i°  east  and  west  of  each  stan- 
dard meridian. 

403.  The   Earth  makes  one  revolution  in  24  hours.     Its 

circumference  is  360°.     360°  -r-  24  =  15°  the  distance  passed  in 
1  hour. 


122  MODERN    BUSINESS    ARITHMETIC 

404.  If  a  point  on  the  earth  passes  15°  in  1  hour  or  60  min- 
utes, in  1  minute  it  will  pass  -fa  of  15°  or  15'.     In   1  minute  or 
60  seconds  it  passes  15';  in  1  second  it  will  pass  ^0  of  15'  or  15". 

405.  Another  analysis  is :     If  a  point  on  the  earth  passes 
15°  in  60  minutes,  to  pass  1°  would  take  iV  of  60  minutes  or  4 
minutes.     If  it  passes  15'  in  60  seconds,  to  pass  l'  would  take  iV 
of  60  seconds  or  4  seconds. 

406.  To  Find  the  Difference  in   Time  when   the 
Difference  in  Longitude  is  Given. 

Divide  the  difference  of  longitude  by  15,  and  the  result  will  be 
the  difference  in  time ;  or  multiply  the  difference  in  longitude  by  4, 
.and  the  result  will  be  minutes  and  seconds. 

EXAMPLE  :  Find  the  difference  of  time  between  New  York 
and  Chicago. 

Chicago  is  87°  27'  45"  west 
New  York  is  74      3     0    west 
Dif .  of  Long.  15)  13   24  45 

0  hr.  53  min.  39  sec. 

Or,  Dif.  in  Long.  13°  24'  45" 

4 

Dif.  in  Time   53  min.  39  sec.  0  rem. 

407.  To  Find  the  Difference  of  I/ongitude  when 
the  Difference  of  Time  is  Given. 

Multiply  the  difference  in  time  by  15,  and  the  result  will  be  the 
difference  in  longitude ;  or  divide  the  difference  in  time  expressed 
in  minutes  and  seconds  by  4,  and  the  result  will  be  the  difference  in 
longitude. 

EXAMPLE  :  Find  the  difference  of  longitude  between  Boston 
and  San  Francisco,  the  difference  of  time  being  3  hours  25  min- 
utes 33  seconds. 

Dif.  in  Time  3  hr.  25  min.  33  sec. 

15 

51°      23'  15"  Dif.  in  Longitude- 

Or,  3  hr.  25  min.  33  sec. 

Reduce  hr.  to  min.  4)  205  min.  33  sec. 

51°    23'    15"  Dif.  in  Longitude. 


LONGITUDE  AND  TIME  123 

408.  The  following  table  gives  the  longitude  of  some  of  the 
principal  cities  of  the  world  : 

Albany  73°  44'  50"  W.  New  Orleans       90°    3'  0"W. 

Astoria,  124°    0'     0"  W.  Omaha                95°  56'  14"  W. 

Boston  71°    3'  30"  W.  Paris                      2°  20'  0"  E . 

Berlin  13°  23'  45"  E .  Philadelphia       75°    9'  3"W. 

Bombay  72°  54'     0"  E .  Rome                  12°  27'  0"  E . 

Cincinnati  84°  29'  32"  W.  Rio  Janeiro         43°  20'  0"W. 

Chicago  87°  37'  45"  W.  San  Francisco  122°  26'  45"  W. 

Detroit  83°    3'     0"  W.  St.  Paul              95°    4'  55"  W. 

Honolulu  157°  52'     0"  W.  St.  Louis            90°  15'  15"  W. 

Mexico  99°    5'     0"  W.  Salt  Lake  City  111°  53'  47"  W. 

New  York  74°     3'     0"  W.  Washington        77°    0'  15"  W. 

409.  In  finding  the  difference  of  the  longitude  of  two  places, 
subtract  if  both  are  east  or  west  longitude ;  add  if  one  is  east 
and  the  other  west. 

410.  Solve  the  following  : 

1     Find  the  difference  in  the  time  of  Boston  and  Chicago. 

2.  Between  Detroit  and  Omaha. 

3.  When  it  is  noon  at  Washington  what  time  is  it  in  San 
Francisco  ? 

4.  When  it  is  noon  at  Philadelphia,  what  time  is  it  at  Paris  ? 

5.  When  it  is  6:30  P.  M.  in  Rome,   what  time  is  it  in  San 
Francisco  ? 

6.  In  traveling  from  Chicago  west,  my  watch  gained  2  hours 
15  minutes  30  seconds.     What  was  my  longitude  ? 

7.  Since  starting  on  my  journey,  my  watch  has  lost  1   hour 
32  minutes  45  seconds.     Which  way  did  I  travel  and  what  was 
the  difference  of  longitude  ? 

8.  I  started  from  Salt  Lake  City  at  9:15  A.   M.,    and  after 
traveling  two  days  found  my  watch  had  lost  1  hour  49  minutes 
37  seconds.     What  direction  had  I  traveled,  and  what  large  city 
has  the  same  longitude  as  my  destination  ? 

9.  What  is  the  difference  of  time  between  Bombay  and  Hon- 
olulu ? 

10.     In  sailing  from  San  Francisco  to  Bombay,  will  a  chro- 
nometer gain  or  lose  time,  and  how  much  ? 


124  MODERN    BUSINESS    ARITHMETIC 

HOME  WORK-NO.  14 

NOTE — Questions  should  be  answered  in  writing. 

1.  Why  multiply  by  15  in  reducing  longitude  to  time,   and 
why  does  this  number  hold  good  as  regards  minutes  and  seconds. 

2.  Why  add  in  some  instances  and  subtract  in  others  in  find- 
ing the  difference  of  longitude  between  two  places  ? 

3.  What  is  the  longitude  and  latitude  of  your  home  city  from 
London  ?     From  Washington  ? 

4.  What  is  the  difference  of  time  between  your  home  city  and 
London  ?     Your  home  city  and  Washington  ? 

5.  What  is  the  difference  of  time  between   New  York   and 
San  Francisco  ? 

6.  In  traveling  west  from  Boston,  Mass.,  I  find  my  watch  to 
vary  from  correct  time  by  1  hr.  6  min.  17  sec.     What  large  city 
has  the  same  longitude  as  my  destination  ? 

7.  When  it  is  noon  in  Philadelphia,   what  time  is  it  at  St. 
Louis,  Mo.? 

8.  When  it  is  4  P.  M.  in  St.  Paul,  what  time  is  it  in  Wash- 
ington, D.  C.  ? 

9.  Will  a  chronometer  gain  or  lose  and  how  much  in  travel- 
ing from  Rome  to  Omaha  ?. 

10.  The  great  earthquake  at  San  Francisco  occurred  April  18, 
1906,  at  5:15  A.  M.  Had  the  news  been  telegraphed  to  New 
York  without  loss  of  time  at  what  hour  should  it  have  been  re- 
ceived ? 


Denominate  Fractions 

411.  Denominate  Fractions  may  be  reduced  from  one 
denomination  to  another  by  the  same  operations  and  principles 
which  apply  to  denominate  numbers. 

412.  To  Reduce  a  Denominate  Fraction  or  Deci- 
mal to  Lower  Denominations. 

Multiply  by  the  number  of  units  of  the  next  lower  denomination 
required  to  make  one  of  the  given  fraction  or  decimal.  If  there  be 
a  fractional  remainder,  treat  it  'in  the  same  manner. 

EXAMPLE  :     Reduce  £  of  a  £>  to  lower  denominations. 


EXAMPLE:     Reduce  ,£.190625  to  lower  denominations. 

£.  190625                       .8125s.  .75d. 

_  20  _  12  _  4 

3.812500s.  9.7500d.  3.00  far. 
Answer,  3s.  9d.  3  far. 

413.     Solve  the  following  : 

1.  Reduce  £%2  to  lower  denominations. 

2.  Reduce  .£.31875  to  lower  denominations. 

3.  Reduce  %2  of  a  rod  to  lower  denominations. 

4.  Reduce  .245  mi.  to  lower  denominations. 

5.  Reduce  .54375  Ibs.  Troy  to  lower  denominations. 

6.  Reduce  .365375  T.  Avoirdupois  to  lower  denominations. 

7.  How  many  acres  in  .375  of  a  section? 

8.  How  many  gills  in  %e  of  a  gallon  ? 

9.  A  sold  Vs  of  %  of  .75  of  a  ton  of  coal  for  $5.     What  was 
the  selling  price  per  cwt. 

10.     How  many  sq.  1.  in  .012345  of  an  acre? 


126  kODERN    BUSINESS    ARITHMETIC 

414.  To  Reduce  a  Denominate  Fraction  or  Deci- 
mal to  a  Higher  Denomination. 

Divide  by  the  number  of  units  required  to  make  one  of  the  higher 
denomination. 

EXAMPLE  :     Reduce  ^  minute  to  days. 

I  X  -sV  X  T¥  =  TsVo  days. 
EXAMPLE  :     Reduce  .64  quarts  to  bushels. 

.64 -f-  (8  X  4)  =  .02bu. 

415.  Solve  the  following  : 

1.  Reduce  %  pt.  to  gallons. 

2.  Reduce  %  ft.  to  yards. 

3.  What  fraction  of  a  bushel  is  %  of  a  quart  ? 

4.  What  fraction  of  a  mile  is  %2  of  a  rod? 

5.  What  decimal  of  a  ton  is  45  Ib  ? 

6.  What  decimal  of  a  day  is  10.8  minutes? 

7 .  What  part  of  a  mark  is  %  pfennig  ? 

8.  Reduce  .33%  of  a  shilling  to  the  fraction  of  a  £. 

9.  Three-fourths  of  a  Ib.  Avoirdupois  is  what  fraction  of  a 
bushel  of  wheat  ? 

10.     One-third  of  B's  age  equals  %  of  A's.     If  the  sum  of  their 
ages  is  .75  of  52  years,  what  is  the  age  of  each  ? 

416.  To  Reduce  a  Denominate  Number  to  a  Deci- 
mal or  Fraction  of  a  Higher  Denomination. 

Reduce  the  denominate  numbers  by  dividing  the  lowest  first,  and 
successively  the  others,  annexing  the  fractional  part  at  each  change 
in  denomination. 

EXAMPLE  :  Reduce  13  hours  30  minutes  to  the  fraction  of  a 
day.  To  decimal  of  a  day. 

FRACTION  :  DECIMAL  : 

30  min.  X  6V  =  \  hr.  60)  30  min. 

13i  hrs.  =  -V-  hrs.  .5  hr. 

-V-  hrs.  X  21!-  =  A  da.  Ans.  13.     hr. 

24)  13.5  hr. 

Ans.,  .5625  days. 


DENOMINATE  FRACTIONS  127 

417.     Solve  the  following  : 

1.  Reduce  2  yd.  2  ft.  6  in.  to  the  fraction  of  a  rod. 

2.  Reduce  87  Ib.  12  oz.  to  the  decimal  of  a  cwt. 

3.  Reduce  2  pk.  5  qt.  1  pt.  to  the  fraction  of  a  bushel. 

4.  Reduce  2  sq.  ft.  117  sq.  in.  to  the  decimal  of  a  sq.    yard. 

5.  What  part  of  4  hours  is  42  minutes  30  seconds? 

6.  What  part  of  a  hhd.  is  10  gal.  2  qt.  1  pt.  2  gi.  ? 

7.  What  part  of  a  f  5  are  f 35  R136  ? 

8.  What  decimal  part  of  a  cwt.  is  Vi  of  22%  Ibs.  ? 

9.  What  decimal  part  of  a  circle  are  18  deg.  20  min.  15  sec.-? 
10.  What  decimal  part  of  a  ream  are  12  qr.  18  sheets  of  paper  ? 


Addition  of  Denominate  Numbers 

418.  To  Add   denominate  numbers  is  to  unite  them  into 
one  sum  whether  simple  or  compound. 

419.  To  Add  Denominate  Numbers. 

Write  like  denominations  in  the  same  columns  ;  add  and  reduce 
each  sum  to  higher  denominations  when  possible. 

EXAMPLE:     £        s.        d.      far. 
4382 


7 
8 

2 
10 

0 
9 

3 

2 

24       24       21       11  sums  of  each  column  . 
Reduced  =  25         5       11         3  Ans. 
420.     Solve  the  following  : 

1.  Add  5  cwt.  46  Ib.  12  oz.,  12  cwt.  9  Ib.  8  oz.,  2  cwt.  25  Ib., 
21  Ib.  10  oz. 

2.  Add  4  da.  21  hr.  36  min.  10  sec.,  14  hr.  24  min.   15  sec., 
2  da.  22  min.,  3  da.  12  hr.  40  sec. 

3.  Add  8  yd.  2  ft.,  5  yd.  1  ft.  3  in.,  2  ft.  9  in:,   3  yd.   2  ft. 
6  in.,  2  ft.  10  in.,  7  yd  1  ft.  8  in. 

4.  Add  2%  hhd.,  36  gal.  3  qt.  1^4  pt.,  %  gal.,  12  qt.  %  pt., 
1  bbl.  3  gal.  3  gi.,  %  qt.  1  gi. 

5.  Add  R)5  57  33,  Ibl2  SlO  35  92,  32  34  9l  gr.15,  tblO  37 
gr.  12,  36  92V2. 


128  MODERN    BUSINESS    ARITHMETIC 

Subtraction  of  Denominate  Numbers 

421.  To  Subtract  denominate  numbers  is  to  find  their  dif- 
ference . 

422.  To  Subtract  Denominate  Numbers. 

Write  like  denominations  in  the  same  columns ;  subtract  as  in 
simple  numbers,  taking  a  unit  of  the  next  higher  denomination 
when  necessary  to  increase  the  minuend. 

EXAMPLE  :     bu.     pk.      qt.      pt. 
4260 
1821 
2331  Ans. 

423.  Solve  the  following  : 

1.  From  25  rd.  2  yd.  2  ft.  6  in.,  take  14  rd.  4  yd.  1  ft.  10  in. 

2.  From  4%  bu.  take  3Vs  bu. 

3.  From  44  cd.  4  cd.  ft.  10  cu.  ft.   take  18  cd.   6  cd.   ft.   14 
cu.  ft. 

4.  From  a  cask  of  cider  containing  44  gal.,  12  gal.  3  qt.  1  pt. 
1  gi.  was  drawn  off.     How  much  remained  ? 

5.  A  sold  from  his  farm,  containing  320  A.,  two  lots  of  land; 
the  first  contained  72  A.  32  sq.  rd.;  the  other   112  A.   4  sq.  ch. 
How  much  did  he  have  left  ? 


Multiplication  of  Denominate  Numbers 

424.  Multiplication  is  a  short  method  of  making  addi- 
tions of  the  same  number. 

0 

425.  To  Multiply  a  Denominate  Number. 

Multiply  as  in  simple   numbers.     Reduce  to  higher  denomina- 
tions when  necessary. 

EXAMPLE  :     Multiply  3  mo.  10  ds.  5  hrs.  20  min.  30  sec.  by  5. 

mo.      ds.       hrs.     min.      sec. 
3         10          5        20        30 

5 

15        50        25       100       150  product. 
Reduced  =  16         21  2         42         30  Ans. 


DENOMINATE  FRACTIONS  129 

Solve  the  following  : 

1.  Multiply  32  rd.  1  yd.  2  ft.  5  in.  by  10. 

2.  Multiply  4  bu.  3  pk.  5  qt.  by  9. 

3.  Multiply  2  gal.  2  qt.  1  pt.  31/i  gi.  by  64. 

4.  If  an  acre  of  land  will  produce  35  bu.  3  pk.  6  qt.  1  pt.  of 
grain,  how  much  will  a  farm  of  1A  section  produce? 

5.  What  will  be  the  cost  of  8  casks  of  vinegar,   each  cask 
containing  42  gal.  3  qt.  1  pt.  at  22  cents  per  gallon? 


Division  of  Denominate  Numbers 

426.  Division  is  the  process  of  finding  one  of  the  equal 
parts  of  a  number. 

427.  To  Divide  a  Denominate  Number. 

Divide  as  in  simple  numbers.     Reduce  remainder  to  lower  denom- 
inations when  necessary. 

EXAMPLE  :     Divide  47  bu.  2  pk.  7  qt.  1  pt.  by  5. 

5)47bu.  2pk.  7qt.  1  pt. 

9211  Answer. 
(  Dividing  and  reducing  each  remainder.) 

428.  Solve  the  following  : 

1.  Divide  426  A.  123  sq.rd.  25  sq.  yd.  7  sq.  ft.  by  12. 

2.  Divide  /44  8s.  lOd.  by  8. 

3.  Divide  320  gal:  3  qt.  1  pt.  3  gi.  by  42. 

4.  How  many  boxes  holding  1  bu.   1  pk.  7  qt.  each  can  be 
filled  from  356  bu.  3  pk.  5  qt.  of  berries? 

5.  A  township    6    miles  square  is  divided  into  farms    each 
containing  153  A.  6sq.  ch.     How  many  farms  were  there? 


Areas  or  Surfaces 


429.     A  Straight  Line  is  one  whose  points  all  lie  in  the 
same  direction. 

A str««ht L,n.  NOTE — A  straight  line  is  the  shortest  distance  be- 
tween  two  points. 

430.  A  Curved  Line  is  one  that  changes 
its  direction  at  every  point. 

431.  Parallel  Lines  are  equidistant  in 
their  entire  length. 

432.  An  Angle  is  the  divergence  of  two 
lines  from  a  common  point. 

433.  A  Right  Angle  is  formed  where 
one  straight  line  meets  another  straight  line 
making  two  equal  angles. 

434.  An  Acute  Angle   is   less  than   a 
right  angle. 

435.  An  Obtuse  Angle  is  greater   than 
a  right  angle. 

436.  A  Quadrilateral  is  a  plain  figure 
having  four  sides  and  four  angles, 

437.  A  Parallelogram  is  a  quadrilater- 
al whose  opposite  sides  are  parallel. 

438.  A  Rectangle  is  a  right-angled  par- 
allelogram. 

439.  A  Square    is    an    equilateral    rect- 
angle. 

440.  A    TrapeZOid    is    a     quadrilateral 
having  only  two  sides  parallel. 

441.  A    Trapezium   is   a  quadrilateral 
whose  opposite  sides  are  not  parallel. 


AREAS  OR  SURFACES 


131 


442.  A  Triangle  is  a  plane  figure  hav- 
ing three  sides  and  three  angles. 

443.  An   Isosceles   Triangle  is  one 

having  two  equal  sides  and  two  equal  angles. 

444.  An  Acute-Angled  Triangle  is 

one  all  of  whose  angles  are  acute. 

445.  An   Obtuse  -  Angled   Triangle 

is  one  having  one  obtuse  angle. 

446.  The  Base  of  a  figure   is   the  side 
upon  which  it  is  supposed  to  rest. 

447.  The  Altitude  is  the  perpendicular 
distance  between  the  base  line  and  the  highest 
point  opposite. 

448.  The   Hypothenuse    of    a    right- 
angled  triangle  is  the  side  opposite  the  right 
angle. 

449.  The  Diagonal  of  a   quadrilateral 
is  a  line  connecting  two  opposite  angles. 

450.  A  Rhomboid  is  an  oblique-angled 
parallelogram. 

451.  A    Rhombus    is     an    equilateral 
rhomboid. 

452.  A  Polygon  is  a  plane  figure  bound- 
by  straight  lines. 

NOTE — Polygons  are  named  from  their  number 
of  sides.  Thus,  one  of  five  sides  is  called  a  PENTA- 
GON ;  of  six  sides,  a  HEXAGON  ;  of  seven,  a  HEPTA- 
GON ;  of  eight,  an  OCTAGON  ;  etc.  • 

453.  The  Perimeter  of   a  polygon  is 
the  total  length  of  its  boundary  lines. 


Pentagon.       Hexagon.         Heptagon.        Octagon.          Nonagon.         Decagoc. 


132  MODERN    BUSINESS    ARITHMETIC 

Surface  Measure 

454.  A    Surface   has   two    dimensions, 
length  and  breadth. 

NOTE — A  square  inch  is  a  rectangular  surface 
whose  length  and  breadth  are  each  ONE  inch. 

455.  The  Area  of  a  surface  is  the  num- 
ber of  square  units  within  its  perimeter. 

NOTE — Thus  a  rectangle  3  inches  wide  and  5 
inches  long  has  three  rows  of  square  inches  with 
four  square  inches  in  a  row,  or  15  square  inches  in 
all. 

456.  To  Find  the  Area  of  a  Rectangle. 

Multiply  the  length  by  the  breadth  expressed  in  the  same  linear 
units. 

457.  Solve  the  following  and  draw  diagram  for  each  : 

1.  Find  the  area  of  a  garden  15l/2  rods  long  by  7l/2  rods  wide. 

2.  A  floor  is  42  ft.  6  in.  long  by  20  ft.   wide.     What  is  the 
area? 

3.  Ten  windows  are  each  9  ft.  by  3  ft.  4  in.     What  is  their 
entire  area  in  square  yards  ? 

4.  A  walk  extends  around  the  outside  of  a  court  20  yds.  wide 
by  80  ft.  long.     If  the  walk  is  3  yds.  wide,  what  is  its  area? 

5.  What  is  the  area  in  square  yards  of  a  tennis  court  10  rods 
long  by  60  feet  wide  ? 

458.  To  Find  the  Area  of  a  Triangle. 

Multiply  the  base  by  one-half  the  altitude ;  or,  multiply  the  alti- 
tude by  one-half  the  base. 

NOTE — Every  rectangle  may  be  divided  into  two  equal  triagles  ;  there- 
fore the  area  of  a  triangle  is  one-half  the  area  of  its  rectangle. 

459.  Solve  the  following  and  draw  diagram  for  each  : 

1.  Find  the  area  of  a  triangle  whose  base  is  12  ft.  and  whose 
altitude  is  17  ft. 

2.  What  is  the  area  of  a  triangle  whose  base  is  25   ft.   and 
whose  altitude  is  32  ft? 


AREAS  OR  SURFACES  133 

3.  The  gable  of  a  house  is  20  ft.  wide  and  8  ft.  high.     How 
many  square  feet  ? 

4.  A  triangular  field  is  15  chains  on  one  side  and  the  perpen- 
dicular distance  from  the  opposite  angle  is  15  rods.     How  many 
acres  in  the  field  ? 

5.  At  $90  per  acre,  what  will  be  the  cost  of  a  farm  bounded 
as  follows  :     Starting  at  a  certain  point  and  measuring  73.54  ch. 
north,  thence  44.82  ch.   west,   thence  southeasterly  in   a  direct 
line  to  the  starting  point  ? 

460.  To  Find  the  Area  of  any  Parallelogram. 

Multiply  its  base  by  its  altitude. 

NOTE — Since  any  quadrilateral  may  be  divided  by  its  DIAGONAL  into 
two  triangles,  the  sum  of  the  areas  of  those  triangles  will  be  the  area  of 
the  quadrilateral. 

461.  Solve  the  following  and  draw  diagram  for  each  : 

1.  Find  the  area  of  an  oblique  angled  parallelogram  whose 
base  is  21  ft.  and  whose  altitude  is  16  ft. 

2 .  Find  the  area  of  a  trapezoid  whose  opposite  sides  are  respect- 
ively 18  ft.  and  24  ft.,  and  whose  altitude  is  7  ft. 

3.  One  side  of  a  field  is  64  chains  long,  the   opposite  and 
parallel  side  is  36  chains  long,  and  the  nearest  distance  between 
these  sides  is  25  chains.     How  many  acres  in  the  field? 

4.  The  diagonal  of  a  trapezium  is  44  feet.     The  perpendicu- 
lar distances  from  this  diagonal  to  the  angles  opposite  are  17  ft. 
and  14  ft.     What  is  its  area? 

5 .  From  a  California  Redwood  tree  a  plank 
72  ft.  long,  72  in.  wide  at  one  end  and  54  in. 
wide  at  the  other  is  sawed.  How  many  square 
feet  in  its  surface  ? 

462.     To  Find  the  Area  of  a  Circle. 

Multiply  the  circumference  by  one-fourth  the 
diameter;  or,  square  the  diameter  and  multiply 
by  .7854  ;  or,  square  the  radius  and  multiply  by 
3.1416. 

NOTE — In  mathematics,  a  circle  is  considered  to 
be  composed  of  an  infinite  number  of  triangles  with 
their  vertices  at  the  center,  and  the  circumference 
the  total  sum  of  their  bases.  One-fourth  the  diam- 
eter equals  one-half  the  altitude  of  the  triangles. 
The  circumference  is  always  3. 1416  times  the  length 
of  the  diameter. 


134  MODERN    BUSINESS    ARITHMETIC 

463.     Solve  the  following  : 

1.  Find  the  area  of  a  circle  whose  circumference  is  314.16 
ft.  and  whose  diameter  is  100  ft. 

2.  How  many  sq.  yds.  in  a  circle  60  ft.  in  diameter? 

3.  The  circumference  of  a  circle  is  636.174  ft.     What  is  its 
area  ?  • 

4.  How  many  acres  in  a  circular  field  surrounded  by  a  race 
course  1  mile  long  ? 

^^^^^^^^^^m        5.     A  plaza  400  ft.  in  diameter  is  sur- 
rounded by  a  walk  20  ft.  wide.     How  many 
J  ;  square  feet  in  the  walk  ? 

|J;  464.     To  Find  the  Lateral  Area  of 

I  a  Prism  or  Cylinder. 

Multiply  the  perimeter  of  the  base  by  the 
length. 

465.  To  Find  the  Lateral  Area 
of  a  Pyramid  or  Cone. 

Multiply  the  perimeter  of  its  base  by  one- 
half  its  slant  height. 

466.  To  Find  the  Lateral  Area  of 
a  Frustum  of  a  Pyramid  or  Cone. 

Multiply  one-half  the  sum  of  the  perimeter 
of  both  bases  by  the  slant  height. 

467.  To   Find    the    Area    of   a 
Sphere. 

Multiply  the  diameter  by  the  circumference; 
or,  square  the  diameter  and  multiply  by 
3.1416. 

468.     Solve  the  following  and  draw  diagram  for  each  : 

1.  What  is  the  total  area,  including  base,  of  a  pyramid  12  ft. 
square'  and  20  ft.  slant  height  ? 

2 .  Find  the  lateral  surface  of  a  frustum  of  a  cone  whose  low- 
er base  is  10  in.,  and  whose  upper  base  is  4  in.  in  diameter,   the 
slant  height  being  24  inches. 


AREAS  OR  SURFACES 


135 


3.  How  many  square  feet  in  a  length  of  stove  pipe  24  inches 
long  and  6  inches  in  diameter  ? 

4.  A  sphere  15  inches  in  diameter  requires  how  many  square 
inches  of  gold  leaf  to  cover  it  ? 

5.  A  State  capitol  has  a  dome  60  feet  in  diameter.     What 
would  be  the  cost  to  gild  it  at  $2.50  per  square  foot  if  it  is  a  per- 
fect hemisphere  ? 

Volumes  or  Solids 

469.     A   Solid  or    Volume  is  anything  that  has  length, 
breadth,  and  thickness. 

470.  A  Rectangular  Solid  is  one 

whose  lateral  surfaces  are  rectangles. 

471.  A  Cube  is  a  rectangular  solid 
whose  surfaces  are  equal  squares. 

472.  A  Prism  is  a  volume 
whose  upper  and  lower  bases  are 
equal  polygons  and  whose  sides 
are  quadrilaterals. 

473.  A  Cylinder  is  a  vol- 
ume   whose    upper    and    lower 
bases  are  equal  circles  and  whose 
lateral  surface  is  curved. 

474.  The  Altitude  of  a  solid  is  the  perpendicular  distance 
from  its  highest  point  to  its  base. 


Triangular  Prism    Rectangular  Prism       Pentangular  Prism  Cylinder 

475.     The  Unit  of  Measure  for  solids  is  the  cube,  the  edge 
of  which  is  a  unit  of  some  known  length. 


136  MODERN    BUSINESS    ARITHMETIC 

476.     A  Frustum  of  a  pyramid  or  cone  is  that  part  of  the 
solid  between  the  lower  base  and  any  other  plane  parallel  to  the 
base. 

477.     A  Sphere  is  a  volume  bounded  by 
I      a  curved  surface  every  point  of  which  is  equi- 
W      distant,  from  the  center. 

478.     A  Pyramid  is  a  volume  having  a  polygon  for  its  base 
and  its  sides  triangles  meeting  at  a  point  called  the  vertex. 


Pyramid  Frustum  of  a  Pyramid  Cone  Frustum  of  a  Cone 

479.  A  Cone  is  a  volume  having  a  circle  for  its  base  and 
tapering  uniformly  to  a  point  called  the  vertex. 

480.  To  Find  the  Contents  of  a  Rectangular  Solid. 

The  product  of  the  length,  breadth,  and  thickness  expressed  in 
the  same  denominations  will  give  the  number  of  cubic  units. 

481.  Solve  the  following  : 

1.  What  are  the  solid  contents  of  a  block  of  granite  8  ft.  long, 
3  ft.  wide,  and  2  ft.  thick? 

2.  Find   the  solid    contents  of   a   cube  whose  length  is  33 
inches. 

3.  What  are  the  solid  contents  of  a  cube  whose  superficial 
area  is  726  square  inches? 

4.  A  watering  trough  is  11  ft.  long,  21  in.  wide,   and  18  in. 
deep.     How  many  gallons  will  it  hold? 

5.  Reckoning  a  cubic  foot  equal  to  %  bushels,   how  many 
bushels  of  wheat  will  a  bin  12  ft.  long,  8  ft.  wide,  and  5  ft.  deep 
hold? 


AREAS  OR  SURFACES  137 

481.  To  Find  the  Volume  of  a  Prism  or  Cylinder. 

Multiply  the  area  of  the  base  by  the  altitude. 

482.  Solve  the  following  : 

1.  A  column  of  stone  is  2  ft.   6  in.  square  and  16  ft.   high. 
What  are  its  solid  contents  ? 

2.  What  is  the  volume  of  a  shaft  12  ft.  by  15  ft.   and  90  ft. 
high,  and  what  would  it  cost  at  $.3lM*  per  cubic  ft.  to  erect  it? 

3.  A  mining  shaft  was  300  ft.  deep  and  6  ft.  square.     What 
was  the  cost  of  excavating  and  timbering,   excavations  costing 
$3.50  per  cu.  yd.,  and  timbering  45  cents  per  sq.   ft.   of  lateral 
area? 

4.  A  triangular  prism  is  25  in.  high;  its  base  is  right  angled, 
4  in.  by  3  in.  by  5  in.     What  are  its  contents? 

5.  What  are  the  solid  contents  of  a  hollow  cylinder  4  ft.  long 
and  20  inches  in  diameter,  the  hollow  being  10  inches  in  diam- 
eter? 

483.  To  Find  the  Volume  of  a  Pyramid  or  Cone. 

Multiply  the  area  of  the  base  by  l/s  the  altitude. 

484.  Solve  the  following  : 

1.  What  are  the  solid  contents  of  a  pyramid  5  ft.  square  at 
the  base  and  9  ft.  high? 

2.  What  are  the  solid  contents  of  a  rectangular  pyramid  the 
base  of  which  is  20  ft.  by  30  ft.  and  whose  altitude  is  104  ft.  ? 

3.  Find  the  volume  of  a  cone  whose  base  is  24  ft.   in  diam- 
eter and  whose  height  is  60  ft. 

4.  A  pyramid  75  ft.  high  and  20  ft.  square  at  the  base  is  cut 
off  25  ft.  from  the  top.     What  are  the  solid  contents  of  the  re- 
maining frustum  ? 

5.  Reckoning  144  cu.  in.  to  a  board  foot,   how  many  board 
feet  of  timber  in  a  telegraph  pole  8  in.  square  at  the  base,   4  in. 
square  at  the  top  and  30  ft.  high  ? 


138  MODERN    BUSINESS    ARITHMETIC 

485.     To  Find  the  Volume  of  a  Sphere. 

Multiply  its  superficial  area  by  1/3  its  radius ;  or,   multiply  the 
cube  of  its  diameter  by  .5236. 

1.  Find  the  solid  contents  of  a  solid  shot  4  in.   in  diameter. 

2.  What  are  the  contents  of  a  sphere  whose  diameter  is  10 
feet? 

3.  An  orange  is  15.708  in.  in  circumference.    How  many  cu. 
in.  in  its  contents? 

•  4.     The  earth  is  8000  miles  in  diameter.     How  many  cubic 
miles  in  its  solid  contents  ? 

5.     A  spherical  cannon  shell  is  9  in.   in  diameter  and  1  in. 
thick.     How  many  cubic  inches  of  solid  metal  in  it  ? 


HOME  WORK— No.  15 

1.  How  many  acres  in  a  rectangular  farm  72  rods  wide  by  72 
chains  long  ? 

2.  A  park  is  in  the  form  of  a  rightangled  triangle,  the  base 
being  40  rods  and  the  altitude  30  rods.     How  many  acres  ? 

3.  A  piece  of  cardboard  is  cut  so  that  its  opposite  sides  are 
parallel.     Their  lengths  are  21  in.  and  25  in.,   and  the  perpen- 
dicular distance  between  them  is  15  in.     What  is  its  area? 

4.  How  many  square  yards  in  a  circular  garden  200   feet  in 
diameter  ? 

5.  Find  the  number  of  square  feet  of  radiation  of  a  2-inch 
steam  pipe  32  feet  long. 

6.  How  many  cubic  feet  in  a  column  of  granite,  5  ft.  square 
and  24  ft.  high  ? 

7.  A  cistern  is  4  ft.  by  5   ft.    6   in.,    and  6   ft.   deep.     How 
many  gallons  of  water  will  it  hold  ? 

8.  How  many  feet  of  lumber  in  a  40-foot  telegraph  pole  10 
in.  square  at  the  bottom,  and  4  in.  by  10  in.  at  the  top? 

9.  A  liberty  pole  is  150  ft.   high,    12   in.   in  diameter  at  the 
base,  and  tapers  to  a  point.     What  is  its  weight  at  30  Ibs.  per 
cubic  foot  ? 

10.  What  is  the  weight  of  a  leaden  casket  12  in.  long,  6  in. 
wide,  and  4  in.  thick,  the  lead  on  all  six  sides  1  in.  thick  and 
weighing  1  Ib.  to  every  3  cubic  inches? 


MODERN  BUSINESS  ARITHMETIC  139 

Relation  of  Measurements 

486.  Similar  Lines,  Areas,  and  Volumes  have  relation 
according  to  the  following  principles  : 

NOTE— For  full  discussion  of  the  subject  of  proportion  see  page  148. 

PRIN.      I.      Corresponding  lines  of  similar  figures  are  in  pro- 
portion. 

EXAMPLE  :  What  is  the  width  of  a  rectangle  42  feet  long  if 
a  similar  one  is  5  feet  by  14  feet  ? 

Length  :  Breadth  ::  Length  :  Breadth 
42  ft.       :  (     )  ft.    ::  14  ft.       :  5  ft. 
42  times  5  divided  by  14  equals  15,  No.  ft.  in  width. 

PRIN.     II.      Similar  areas  are  in  proportion  as  the  squares  of 
their  like  dimensions. 

NOTE— The  square  of  a  number  is  its  product  when  used  twice  as  a  factor.  As,  3 
times  3  equals  9. 

EXAMPLE  :  If  a  rectangle  whose  base  is  18  feet  contains  162 
square  feet,  what  will  be  the  area  of  a  similar  rectangle  whose 
base  is  12  feet? 

Area  :  (Base)8  ::  Area  :  (Base)3 

162  sq.ft.  :  (18)8       ::  (      )  :  (12)8 
162  times  (12) 2  divided  by  (18) 8  equals  72,  No.  sq.  ft.  in  area. 

PRIN.  III.      Similar  volumes  are  in  proportion  as  the  cubes  of 
their  like  dimensions. 

NOTE— The  cube  of  a  number  is  its  product  when  used  three  times  as  a  factor.  As,  3 
times  3  times  3  equals  27. 

EXAMPLE  :  If  a  rectangular  solid  6  inches  long  contains  60 
cubic  inches,  what  will  be  the  contents  of  a  similar  volume  12 
inches  in  length  ? 

Volume      :  (Length)3  ::  Volume  :  (Length)3 
60  cu.  in.  :  (6)3  ::  (  )  :  (12)3 

60  times  (12) 3  divided  by  (6)3  equals  480,  No.  cu.  in.  in  volume. 


PRACTICAL  PROBLEMS 

1.  If  a  block  of  granite  4  ft.  thick  weighs  2  tons,  what  will  a  similar 
one  8  ft.  thick  weigh? 

2.  If  the  diagonal  of  a  rectangular  garden  whose  area  is  12  sq.  rd.  is 
82  ft.  6  in.,  what  is  the  area  of  a  similar  one  whose  diagonal  is  15  rds.  ? 

3.  If  a  leaden  shot  2  in.  in  diameter  weighs  2  Ibs.,  what  should  be  the 
weight  of  one  4  in.  in  diameter? 

4.  If  a  reservoir  can  be  emptied  by  a  3  in.  pipe  in  12  hours,  how  long 
will  it  take  a  4  in.  pipe  to  empty  it? 

5.  If  a  man  5  ft.  tall  weighs  150  Ibs.,  what  will  be  the  weight  of  one 
of  similar  build  who  is  6  ft.  tall  ? 


Practical  Measurements 


Plastering,  Painting,  Papering,  Carpeting,  Etc. 

487.  Plastering  is  computed  by  the  square  yard  ;  painting  by 
the  square  yard,  or  by  the  square  of  1000  square  feet ;    paving 
by  the  square  yard,   or  square  foot ;  carpeting  by  the  square 
yard,  or  by  the  lineal  yard,  and  papering  by  the  roll,   which  is 
usually  8  yards  long  and  18  inches  wide. 

488.  In  computing  the  cost  of  materials,   make  allowances 
for  openings,  but  in  computing  the  cost  of  labor,  make  no  such 
allowances,  except  when  called  for  in  the  contract. 

EXPLANATION  :  This 
diagram  represents  the 
plan  of  the  first  floor  of 
a  house  whose  extreme 
outside  measurements 
are  36  feet  by  42  feet. 

ROOMS  :  The  dimen- 
sions of  the  rooms  are 
given  on  the  diagram ; 
the  height  from  floor  to 
ceilings  is  12  feet. 

OPENINGS:  The  open- 
ings will  average  two 
square  yards  each,  ex- 
cept the  archways  be- 
tween the  Jhall  and  re- 
ception room  and  be- 
tween the  hall  and  li- 
brary, which  are  four 
square  yards  each. 

SECOND  STORY  :  The 
dimensions  of  the  four 
rooms  of  the  second 
story  are  given  on  the 
diagram  for  the  second 
floor  plan.  The  height 
from  floor  to  ceilings  on 
this  floor  is  10  feet. 

489.  Solve  the  following  : 

1.  Find  the  cost  of  plastering  the  reception  room  in  the  fore- 
going diagram,  walls  and  ceiling,  at  30  cents  a  sq.  yd.,  deduct- 
ing one-half  the  area  of  the  openings. 


FIRST    FLOOR 


PRACTICAL  MEASUREMENTS 


141 


2.  Find  the  cost  of  plastering  the  library  walls  and  ceilings, 
at  30  cents  a  sq.  yd.,  deducting  one-half  the  area  of  the  open- 
ings, and  allowing  for  3-foot  wainscoting. 

3.  Find  the  cost  of  plastering  and  paneling  the  dining-room, 
the  paneling  to  be  7  ft.  high  and  to  cost  12^2  cents  per  sq.   ft., 
the  top  of  the  walls  and  the  ceiling  to  be  plastered  and  stuccoed 
at  50  cents  per  sq.  yd.,  allowing  a  reduction  of  one-half  of  area 
of  openings,  all  in  the  paneling. 

4.  Find  the  cost  of 
hardfinishing  the  kitch- 
en   and   serving   room 
at  40  cents  per  sq.  yd., 
and  providing  for  a  four 
foot   tile    wainscoting, 
costing  25^  per  sq.  ft., 
no  allowances  for  open- 
ings in  plastering,  but 
100  sq.   ft.  allowed  for 
openings  in  tiling. 

5.  Find  the  cost  of 
plastering      the      four 
chambers  of  the  second 
story  at  35   cents   per 
sq.  yd.,  deducting  one- 
half  of  the  area  of  the 

SECOND    FLOOR  OpCllingS. 

6.  Find  the  cost  of  flooring  the  second  story  of  this  building 
(35  ft.  x  35  ft.)  with  Oregon  pine  costing  $42  per  M.,  allowing 
one- fourth  for  matching  and  waste,  and  no  deductions  made  for 
walls. 

7. .  Find  the  cost  of  flooring  with  eastern  oak  at  15  cents  per 
sq.  ft.,  actual  measurement,  of  reception  room,  library,  dining- 
room,  and  hall  (  200  sq.  ft  ). 

8.  Find  the  cost  of  tinting  library  and  reception  room  at  15 
cents  per  sq.  yd.,  allowing  for  wainscoting  in  library  and  12  in. 
base-boards  in  reception  room. 


142  MODERN    BUSINESS    ARITHMETIC 

9.  What  will  be  the  cost  of  papering  the  walls  and  ceilings  of 
the  four  chambers  with  wall  paper  costing  55  cents  per  roll  and 
the  ceiling  paper  35  cents  per  roll,  no  allowance  to  be  made  for 
openings  ? 

10.  What  will  be  the  entire  cost  of  carpeting  the  house  as  fol- 
lows :  Reception  room  rug,  9  x  12  ,  costing  $2.25  per  sq.  yd.  ; 
library  rug,  12  x  18,  costing  $2.50  per  sq.  yd.  ;  dining-room 
rug,  11  x  16  ,  costing  $1.80  per  sq.  yd.  ;  kitchen  linoleum,  cov- 
ering entire  floor,  costing  $1.50  per  sq.  yd.  ;  four  hall  rugs, 
costing  $7.50  each  ;  34  yards  stair  and  hall  carpet,  costing  $1.50 
per  yd.  ;  carpet  for  all  four  chambers,  covering  entire  floors,  27 
in.  wide,  strips  to  run  longest  way  of  the  room,  and  costing 
$1.20  per  lineal  yard?  No  allowance  to  be  made  for  waste. 


Brick,  Stone,  Concrete,  and  Excavations 

490.  Brick  Work  is  estimated  by  the  number  of  bricks  re- 
quired to  build  the  walls.     If  the  wall  is  only  one  brick   or  four 
inches  thick,   seven  common  sized  brick  are  required  for  each 
square  foot  of  superficial  area ,   fourteen  bricks  are  required  if 
two  bricks  thick;  twenty-one,  if  three  bricks  thick,  etc. 

491.  Stone  is  estimated  by  the  perch  which   is   16%   feet 
long  18  inches  wide,   and  1   foot  thick,   containing  24%  cubic 
feet..    Cut  stone  is  sometimes  estimated  by  the  surface  square 
foot. 

492.  Concrete  pavements  are  estimated  by  the  square  foot; 
solid  walls  by  the  cubic  foot,  or  by  the  perch. 

493.  When  material  alone  is  to  be  estimated,   allow  for  all 
corners  and  openings.     When  labor  alone  is  to  be  estimated, 
make  no  allowances  unless  by  special  contract.     When  a  gen- 
eral estimate  on  material  and  labor  together  is  to  be  made,   use 
exterior  measurements  and  allow  one-half  for  openings. 


PRACTICAL  PROBLEMS 
494.     Solve  the  following  : 

1.     What  will  be  the  cost  of  a  6-foot  concrete  sidewalk  across 
the  front  of  a  50-ft.  lot,  at  17  cents  per  sq.  ft.  ? 


PRACTICAL  MEASUREMENTS  143 

2.  What  will  be  the  cost  of  a  concrete  foundation  24  in.  wide 
across  the  base,  12  in.  across  the  top,    and   18  in.   deep,    for  a 
house  36  ft.  square,  at  12V2  cents  per  cu.  ft.  ? 

NOTE — Estimate  the  length  of  wall  to  be  the  same  as  the  perimeter  of 
the  building,  144  feet. 

3.  How  many  common  bricks  in  a  13-in.  fire  wall  92  ft.  long 
and  30  ft.  high  ? 

4.  What  will  be  the  cost  of  building  a  brick  smoke-house  12 
ft.  square  and  8  ft.  high,  the  walls  to  be  two  bricks  thick?     No 
allowances  ;  material  and  labor  to  cost  $24.50  per  M.  ? 

5.  What  will  be  the  cost  of  the  basement  walls  to  rest  on  the 
concrete  foundation  in  problem  No.   2  above,   walls  to  be  three 
bricks  thick,  5  ft.  high,  and  36  ft  by  36  ft.  full  size  of  the  build- 
ing; the  brick  to  cost  $15  per  M.  ;  allowance  made  for  corners, 
also  7  openings  3ft.  by  4  ft.  ;  the  labor  to  cost  $5.  per  M.   with 
no  allowances  ? 

6.  Find  the  cost  of  excavating  a  cellar,  18  ft.   by  36  ft.   and 
6  ft.  deep,  at  60  cents  per  cu.  yd. 

7.  Fiud  the  cost  of  building  the  four  walls  to  the  above  cel- 
lar, walls  to  be  12  in.  thick,  at  $2.25  per  perch. 

8.  At  17  cents  per  sq.  ft.  for  concrete  floor,  and  30  cents  per 
sq.  yd.  for  cement  walls,  what  would  be  the  cost  of  finishing  the 

.  above  cellar  ? 

9.  Find  the  cost  of  digging  and  walling  the  cellar  of  a  house 
whose  length  is  41  ft.  3.  in.  and  whose  width  is  33  ft.;   the  cel- 
lar to  be  8  ft.  deep,  and  the  wall  l^ft.   thick.     The  excavating 
will  cost  $.50  a  load,  and  the  stone  and  mason  work  $3.75   a 
perch. 

10.  How  many  common  bricks  will  it  take  to  build  the  four 
exterior  walls  of  a  house  36  ft.  by.  36  ft.;  the  walls  to  be  20  ft. 
high  and  3  brick  thick,  allowing  for  28  openings  averaging  3  ft. 
by  7  ft.,  also  for  the  four  corners ;  and  what  would  be  the  total 
cost  at  $18  per  thousand  bricks  ? 


144  MODERN    BUSINESS    ARITHMETIC 

Wood  and  I/umber 

495.  A  Cord  of  wood  is  8  ft.  long,  4  ft.  wide,   4  ft.  high, 
and  contains  128  cu  ft. 

496.  Lumber  is  measured  by  the  board  foot  which  is  12  in. 
square  and  1  in.  thick. 

497.  Iy umber  less  than  1  in.  thick  is  estimated  as  though  an 
inch  in  thickness.     If  more  than  1  in.  thick,  a  proportionate  in- 
crease is  estimated. 

498.  To  Find  the  Number  of  Board  Feet  in  any 
Piece  of  I/umber. 

Multiply  the  length  infect  by  the  width  and  thickness  in  inches 
and  divide  by  12. 


PRACTICAL  PROBLEMS 

499.     Solve  the  following  : 

1.  Find  the  number  of  cords  of  wood  in  a  pile  4  ft.   wide,   6 
ft.  high,  and  24  ft.  long. 

2.  How  many  cords  of  wood  in  a  pile  48   ft.   long  on  the 
ground,  36  ft.  on  the  top,  4  ft  wide,  and  6  ft.  high? 

3.  How  many  feet  of  lumber  in  a  board  16  ft.  long,   10  in. 
wide,  and  1  in.  thick? 

4.  How  many  feet  of  lumber  in  60  boards  14  ft.  long,    8  in. 
wide,  and  1  in.  thick? 

5.  Find  the  contents  of  a  board  18  ft.   long,  20  in.  wide  at 
one  end  and  14  in.  at  the  other,  and  1  in.  thick. 

6.  Find  the  cost  of  180  planks  24  ft.  long,   14  in.  wide,   and 
3  in.  thick,  at  $27  per  M. 

7.  Find  the  cost  of  flooring  a  two-story  house,   36  ft.  by  36 
ft.,  at  $30  per  M.,  the  flooring  to  be  1^  in.   thick,   allowing  % 
for  matching  and  waste. 


PRACTICAL  MEASUREMENTS  145 

8.  Find  the  cost  of  the  following  bill  of  lumber : 

120  pcs.  15  ft.  by  10  in.  @  $21  per  M. 
240            14  ft.         12  in.  22 

64  18  ft.    "    2x4  in.  18 

88  12  ft.    "    2x12  in.  20 

160  18  ft.    "    2x6  in.  20 

9.  A  field  16  ch.  long  by  8  ch.  wide  is   enclosed  by  a  board 
fence  5  boards  high ;  the  boards  are  16  ft.  long  and  6  in.   wide, 
supported  by  posts  every  8  feet.     The  lumber  for  fencing  cost 
$20  per  M.,  and  the  posts  $10  per  C.     What  was  the  cost  of 
lumber  and  posts  to  fence  the  field? 

10.  How  many  shingles  will  it  take  to  shingle  a  roof  60  ft. 
long,  the  girt  from  eaves  to  eaves  over  the  ridge  of  the  roof  be- 
ing 48  ft.  ;  the  shingles  laid  4  in.  to  the  weather,  and  the  eave 
rows  doubled.. 

NOTE — A  shingle  is  4  inches  wide  or  3  to  the  lineal  foot. 


Capacity  of  Bins,  Cisterns,  Etc. 

500.  To  find  the  Exact  Contents  of  a  bin  in  bushels,  re- 
duce the  contents  to  cubic  inches  and  divide  by  2150.42,   the 
number  of  cubic  inches  in  a  bushel. 

501.  To  find  the  Approximate  Contents  of   a   bin  in 

bushels,  reduce  the  contents  to  cubic  feet  and  take  %  (or  .8  )  of 
the  result  for  stricken  measure.  For  heaped  measure,  take  %  of 
the  number  of  bushels  of  stricken  measure,  or  .64  of  the  number 
of  cubic  feet. 

NOTE — Corn  in  the  ear,  potatoes,  roots,  and  coarse  articles  are  usually 
measured  by  heaped  measure;  grains  and  fine  articles  by  stricken  measure. 

502.  To  find  the  Exact  Capacity  of  a  tank  or  cistern  in 
gallons,  reduce  the  contents  to  cubic  inches  and  divide  by  231, 
the  number  of  cubic  inches  in  a  gallon. 

503.  To  find  the  Approximate  Contents  of  a  tank  or 
cistern  in  gallons,  reduce  the  contents  to  cubic  feet  and  multiply 
by  7%,  the  number  of  gallons  in  a  cubic  foot. 


146  MODERN    BUSINESS    ARITHMETIC 

PRACTICAL  PROBLEMS 
504.     Solve  the  following  : 

1.  Find  the  exact  number  of  bushels  in  a  bin  8  ft.  4  in.  long, 
6  ft.  8  in.  wide,  and  4  ft.  2  in.  deep. 

2.  Find  the  approximate  contents  of  a  bin  24  ft.  long,   18  ft. 
wide,  and  10  ft.  deep. 

3.  What  must  be  the  depth  of  a  bin  that  is  6  ft.  4  in.  long  by 
4  ft.  6  in.  wide,  that  will  hold  72%  bushels,   approximate  mea- 
sure? 

4.  What  is  the  length  of  a  wagon  box  3  ft.   4  in.   wide,   and 
18  in.  deep  that  will  hold  32%  bu.   of  corn  in  the  ear,   heaped 
measure. 

5.  A   corn  crib  75  ft.   long,   10  ft.  wide,   and  10  ft.   deep, 
is  filled  \vith  corn  in  the  ear.     What  should  it  bring  at  60  cents 
per  bushel,  if  2  bushels  of  corn  in  the  ear  are  equal  to  one  bushel 
of  shelled  corn  ? 

6.  What  is  the  exact  contents  in  gallons  of  a  tank  4  ft. 
square  and  5  ft.  3  in.  deep? 

7.  Find  the  number  of  barrels  a  cistern  6  ft.  square  and  8  ft. 
deep  will  hold,  exact  measure. 

8.  Find  the  approximate  number  of  gallons  in  a  watering 
trough  12  ft.  long,  24  in.  wide,  and  18  in.  deep. 

9.  How  many  barrels  will  a  circular  cistern  7  ft.   6  in.  deep 
and  6  ft.  in  diameter  hold,  approximate  measure  ? 

10.  What  must  be  the  depth  of  a  reservoir  that  will  hold 
3,000,000  gallons  of  water,  its  length  being  200  ft.  and  its  width 
100  ft.  ? 


Ratio  and  Proportion 

Ratio 

505.  Ratio  is  the  relation  between  two  numbers. 

506.  The  Terms  of  a  ratio  are  the  numbers  compared. 

507.  The  Antecedent  is  the  first  term,  the  dividend. 

508.  The  Consequent  is  the  second  term,  the  divisor. 

509.  The  Sign  is  the  colon  (:)  and  is  read  "  is  to" 

510.  The  Value  of  a  ratio  is  the  quotient  obtained  by  divid- 
ing the  antecedent  by  the  consequent.     Thus,  the  ratio  of  18  to  3 
is  6,  or  18  :  3  =  6. 

511.  A  Simple  Ratio  is  the  ratio  between  two  numbers 
only;   as  14  :  7. 

512.  A  Compound  Ratio  is  the  ratio  of  two  sets  or  groups 
of  simple  ratios  whose  products  must  be  taken.     Thus, 

-JQ  \  t  \  =  60  :  10  ==  6,  value  of  the  compound  ratio. 

513.  Solve  the  following  : 

1.  What  is  the  ratio  of  42  to  7  ?     Of  96  to  12  ? 

2.  The  antecedent  is  324;  the  consequent  9.     What  is  the 
ratio  ? 

3.  The  antecedent  is  5  ;  the  consequent  is  45.     What  is  the 
ratio  ? 

4.  The  antecedent  is  243  ;  the  ratio  is  27.     What  is  the  con- 
sequent ? 

5.  The  consequent  is  35  ;  the  ratio  is  7.     What  is  the  ante- 
cedent ? 

6.  What  is  the  ratio  of  25  bu.  to  10  pks.  ? 

7.  What  is  the  ratio  of  25  Ib.  11  oz.  4  pwt.  to  19  Ibs.  5  oz.  8 
pwt.  ? 


8.     What  is  the  ratio  of          to  *  °f 


148  MODERN    BUSINESS    ARITHMETIC 

9.     Find  the  value  of  the  compound  ratio,  (10  :  35)  X  (4  :  28) 
X  (7  :  15). 
10.     Find  the  value  of  the  compound  ratio,  (•§•:•§•)  X  (f:f) 


Proportion 

514.  Proportion    is    an    equality  of  ratios.     Thus,    12  :  4 
=  21  :  7,  the  ratio  of  each  couplet  being  3. 

515.  The  Sign  of  proportion  is  the  double  colon  (  ::  ),   and 
is  read    '#.?,"  and  expresses  the  equality  of  the  ratios.     Thus, 
3  :  21  ::  5  :  35  is  read  3  is  to  21  as  5  is  to  35. 

516.  The  Terms  of  a  proportion  are  the  two  antecedents 
and  the  two  consequents  of  the  equal  ratios. 

517.  The  Extremes  are  \hzfirst  and  fourth  terms. 

518.  The  Means  are  the  second  and  third  terms. 

519.  PRINCIPLE  :     The  product  of  the  means  of  any  propor- 
tion is  equal  to  the  product  of  the  extremes. 

520.  To  Find  any  Term  of  a  Proportion. 

Divide  the  product  of  the  means  by  the  given  extreme.     Or,    di- 
vide the  product  of  the  extremes  by  the  given  mean. 

521.  Solve  the  following  : 

1.  Find  the  fourth  term  of  the  proportion,  17  :  85  ::  6  :  (  ?  ). 

2.  Find  the  third  term,  6  :  15  ::(?):  75. 

3.  Find  the  second  term,  12  :(?)::  42  :  294. 

4.  Find  the  first  term,  (  ?  )  :  56  ::  19  :  14. 

7  •      Q  )          (    ?8    '18 

5.  Find  the  missing  term,  4  !  10  J   ::   j  (?)  j  40. 

6.  Find  the  missing  term,  $5  :  $17  ::  35  Ib.  :  (  ?  Ib.  ) 

7.  Find  the  missing  term,   10  horses  :  45  horses   ::•  (  ?bu.  ) 
:  25  bu. 

8.  Find  the  missing  term,  7  da.  :  (?  da.)  ::  98  bu.  :  56  bu. 

9.  Find  the  missing  term,  (  ?  )  :  28  men  ::  10  T.  :  140  T. 
10.     Find  the  missing  term,  n  ;  ::     15  A.  :  45  A. 


RATIO  AND  PROPORTION  149 

CAUSE  AND 


522.  Every  Problem  in  proportion  may  be  resolved  into 
Causes  and  Effects. 

EXAMPLE  :  If  4  men  earn  $72  in  1  week,  what  will  10  men 
earn  at  the  same  rate  ?  Here  the  4  men  are  a  cause,  the  $72,  the 
money  earned,  the  effect.  The  10  men  will  be  a  second  cause, 
and  the  second  effect  is  the  number  of  dollars  required.  Thus, 

1st  Cause  :  1st  Effect  ::  2d  Cause  :  2d  Effect 

4  men     :        $72       ::    10  men   :       (?). 
72XO 


4 

NOTE  —  Proportions  in  Cause  and  Effect  may  be  written  : 
'  '  1st  Cause  :  2d  Cause  :  :  1st  Effect  :  2d  Effect 
-4  Men      :    10  Men    ::         $72        :      $180. 

523.  Study  the  conditions  of  each  problem.     Causes  are  like 
quantities.     Effects  are  like  quantities.     Thus,   if  men,   horses, 
time,  money,  etc.,  belong  to  the  first  cause  they  will  also  be 
found  in  the  second  cause.     Effects  usually  include  the  object  and 
all  its  qualities  and  measurements. 

524.  In   Compound  Proportion    there  may  be  several 
elements  in  each  cause  and  also  in  each  effect. 


PROBLEMS  IN  PROPORTION 

525.     Solve  the  following  : 

1.  If  32  Ib.  of  sugar  cost  $1.92,  what  will  75  Ibs.  cost? 

2.  If  12  horses  consume  36  bu.  of  oats  in  a  given  time,   how 
many  horses  will  consume  288  bu.  at  the  same  rate  ? 

3.  If  15  sheep  can  be  bought  for  $62.25,  how  many  sheep 
can  be  bought  for  $398.40? 

4.  What  will  a  pile  of  wood  cost,   40  ft.  long,   4  ft.   wide, 
and  4  ft.  high,  if  a  pile  12  ft.  long,  4  ft.   wide,   and  8  ft.  high 
cost  $28.50? 

5.  If  a  certain  capital  earn  $1500  in  1  yr.  8  mo.,  in  what  time 
will  double  the  capital  earn  $1200  at  the  same  rate  ? 


150  MODERN    BUSINESS    ARITHMETIC 

6.  If  12  men  in  48  da.,  working  10  hr.  to  the  day,  can  build 
a  wall  120  rods  long,  how  many  rods  can  22  men  build  in  60  da., 
working  8  hr.  to  the  day? 

7.  If  10  rms.  of  paper  are  required  to  print  600  copies  of  a 
book  containing  240  pages  each,  32  lines  to  the  page,   averaging 
10  words  to  the  line,  and  5  letters  to  the  word,  how  many  books 
can  be  printed  from  24  rms.  of  paper,  200  pages  to  the  book,   36 
lines  to  the  page,  12  words  to  the  line,  averaging  4  letters  to  the 
word  ? 

8.  If  it  takes  33600  bricks  to  build  a  wall  80  ft.  long,    20  ft. 
high,  and  3  bricks  thick,  each  brick  8  in.  long,  4  in.  wide,   and 
2  in.  thick,  how  many  bricks  12  in.  long,  5  in.  wide,  and  2-Vfc  in. 
thick  will  it  take  to  build  a  wall  120  ft.  long,  30  ft  high,   and   2 
bricks  thick? 

9.  If  4  men  in  7  da.,  working  9  hr.  per  day,  can  dig  a  ditch 
14  rods  long,  3  ft.  wide,  and  32  in.  deep,  how  many  men  would 
have  to  be  added  to  the  crew  in  order  to  dig  it  in  3  da.,  if  the 
ditch  was  widened  to  5  ft.  and  the  men  worked  10  hr.  per  day  ? 

10.  If  8  men  can  do  a  piece  of  work  in  12  da.  how  many  men 
must  be  added  after  the  work  is  %  done  that  it  may  be  com- 
pleted in  2  days  more  ? 


PERCENTAGE 


526.  Percentage    embraces    those  subjects  in   arithmetic 
which  use  100  as  the  basis  of  computation. 

527.  There  are    "Two   classes   of   subjects   in   Percentage : 
1.     Those  in  which  time  is  not  a  factor.     2.     Those   in  which 
time  is  a  factor. 

528.  The  subjects  of  the  First  Class  are  : 

1.  Profit  and  Loss. 

2.  Trade  Discount. 

3.  Commission. 

4.  Stocks  and  Bonds. 

5.  Taxes. 

6.  Duties  or  Customs. 

7.  Insurance. 

529.  The  subjects  of  the  Second  Class  are  : 

1.  Simple  Interest. 

2.  Periodic  Interest. 

3.  Compound  Interest. 
4..  Partial  Payments. 

5.  Bank  Discount. 

6.  True  Discount. 

7.  Domestic  and  Foreign  Exchange.   * 

530.  Per  Cent,  is  a  contraction  of  per  (  by  )  centum  (  hun- 
dred )  and  means  "  by  the  hundred." 

531.  The  Sign  of  Percent  is  % ,  and  is  read  per  cent. 

532.  Per  cent  is  usually  expressed  as  hundredths.     Thus,  5% 
may  be  written  .05,  or  VOTF- 

533.  At  least  Three  Essential  Elements  are  considered 
in  all  applications  of  percentage. 

534.  The  Base  is  the  number  or  quantity  upon  which  the 
percentage  is  computed. 

535.  The  Rate  expresses  the  number  of  hundredths  of  the 
base  to  be  taken. 


152  MODERN    BUSINESS    ARITHMETIC 

536.  The  Percentage  is  the  number  or  quantity  which  is 
a  certain  number  of  hundredths  of  the  base. 

537.  The  Amount  is  the  sum  of  the  base  and  percentage. 

538.  The  Difference  is  the  base  less  the  percentage. 

539.  The  Amount  Per  Cent,  is  100%  plus  the  rate. 

540.  The  Difference  Per  Cent  is  100%  minus  the  rate. 

541.  The  Unit  of  Percentage  is  100%,  or  the  whole; 
therefore  any  rate  that  is  an  aliquot  part  of  100  may  be  reduced 
to  its  lowest  terms,  and  the  fractional  part  taken.     Thus,   if  the 
rate  is  25%,  iVV  reduced  equals  \. 

TABLE  OF  ALIQUOT  PARTS  OF  100% 


50%    =  •$•  1H%  =  i  33i%=i  80%    = 

33i%  =  J  10%    =  TV  66|%  =  |  16|%  = 

25%    =i  9^%=  A:  25%    =i  83i%  =  f 

20%    =  i  8i%    =  A  75%    = 


20%    =  i         37i%  =  | 
=  |          6i%    =  TV         40%    =  |         62i%  - 
=  i          5%      =  A         60%    =  f        87i%  =  | 


CASE  I 

542.  Given,  the  Base  and  Rate  to  find  the  Percentage. 

Multiply  the  base  by  the  rate ;  or,  take  such  a  part  of  the  base  as 
the  rate  is  a  part  of  100. 

FORMULA  :     Base  X  Rate  =  Percentage. 

543.  Solve  the  following  : 

1.  What  is  6%  of  $400?     12%  of  900  Ibs.  ? 

2.  What  is  25%  of  720  bu.  ?     33i%  of  840  tons? 

3.  What  is  12|%  of  936  hrs.  ?     16f  %  of  $1554  ? 

4.  Bonds's  salary  of    $1250    per  year  was  increased   24%  ? 
What  is  his  monthly  salary  ? 

5.  Jones's  income  the  first  year  was  $2500  ;  the  second  year  it 
increased  20%  ;  the  third,  it  decreased  33|%  ;  the  fourth  year 
it  increased  35%.     What  was  his  income  the  fourth  year? 


PERCENTAGE  153 

6.  Prindle  had  $18400  invested  ;    12|%   in  bonds,    20%   in 
in  bank  stock,   15%   in  city  lots,   30%   farm  property,   and  the 
remainder  in  merchandise.     What  was  his  merchandise  invest- 
ment ? 

7.  A  failed  for  $12400.     The  assignee  was  able  to  pay  three 
installments,  the  first  of  20%,  the  second  of  25%,  and  the  third 
of  30% .     What  was  B's  loss  if  A  was  indebted  to  him  $3200  ? 

8.  A  man  owned  %  of  a  business.     He  sold  %  of  his  share 
for  $3000.     The  firm's  gain  for  the  year  was  25%  of  the  capital 
stock.     Find  the  total  gain. 

9.  Cushman  on  Jan.  1st  had  $4200  in  the  bank.     On  April 
1st  he  drew  out  33%%  of  it;  on  May  1st  he  drew  out  142/7%, 
and  on  July  1st  he  drew  out  37%%.     How  much  had  he  left  in 
the  bank  ? 

10.  Olson  bequeathed  his  entire  estate  of  $50000  as  follows : 
20%  to  his  eldest  son,  25%  of  the  remainder  to  his  second  son, 
33%%  of  the  remainder  to  his  daughter,  10%  of  the  remainder 
to  charity,  and  the  remainder  to  his  wife.  How  much  did  the 
wife  receive? 

CASE  II 

544.  Given,  the  Percentage  and  Base  to  find  the  Rate. 

Divide  the  percentage  by  the  base ;  or,  take  such  a  part  of  100 
per  cent,  as  the  percentage  is  a  part  of  the  base. 

FORMULA  :     Percentage  H-  Base  =  Rate. 

545.  Solve  the  following  : 

1.  What  %  of  300  is  150  ?     Of  $900  is  $225  ? 

2.  What  %  of  720  mi.  is  18  mi.  ?     Of  4500  oz.  is  900  Ib.  ? 

3.  What  %  of  24  is  96  ?     Of  $750  is  $2250  ? 

4.  What  %  of  %  is  %  ?     Of  %  is  9/i6  ? 

5.  A  farmer  raised  40  bu.  of  oats  from  1  bu.  of  seed.     What 
%  of  the  crop  was  the  seed  ? 

6.  A  merchant  sold  from  a  barrel  of  molasses  containing  48 
gallons,   %  .of  the  contents  the  first  week,   and  X. tne  second 
week,  and  12%%  the  third  week.     What  %  of  the  original  con- 
tents remained  ? 


154  MODERN    BUSINESS    ARITHMETIC 

7.  A  boy  had  6  doz.  marbles.     He  lost  25%  of  them  the  first 
day;  33%%  of  the  remainder  the  second  day,   and  16%  of  the 
remainder  the  third  day.     What  %  of  the  original  number  did 
he  then  have  ? 

8.  My   stock   of   goods    increased  in  value  10%  ;  then  de- 
creased 20%  ;  then  increased  50%.     If  the  original  value  was 
$1200,  what  is  it  now  worth,  and  what  is  the  %  of  increase? 

9.  A  firm  begins  business  with  $18750  capital.     The  first 
year  they  gain  33%%,  which  amount  is  added  to  their  capital; 
the  second  year  they  lose  10%,  which  is  charged  to  investment; 
the  third  year  they  gain  $4500.     What  is  their   %   of  gain  the 
third  year  ? 

10.  Green  finding  himself  deeply  in  debt,  made  an  assignment 
in  favor  of  his  creditors.  If  his  total  assets  amounted  to  $7945, 
and  his  total  liabilities,  including  $280,  assignee's  costs,  were 
$10500;,  what  rate  %  could  he  pay  his  creditors  ? 


CASE  III 

546.  Given,  the  Percentage  and  Rate  to  find  the  Base. 

Divide  the  percentage  by  the  rate;  or  take  as  many  times  the  per- 
centage as  100%  is  times  the  rate. 

FORMULA  :     Percentage  -=-  Rate  =  Base. 

547.  Solve  the  following  : 

1.  Of  what  is  72   12%%  ?     Is  143    33%%  ? 

2.  Of  what  are  $420   16%%?     Are  $343    25%? 

3.  James  lost  120  ft.  of  his  kite  string  and  then  had  37%% 
left.     What  was  its  original  length  ? 

4.  A  drew  out  20%  of  his  money  from  the  bank  on  July  10th; 
25%  on  Aug.  1st,  when  he  had  $605  left  in  bank.     What  was 
his  original  amount  on  deposit  ? 

5.  Smith  owned  66%%  of  a  business  ;  he  then  sold  25%   of 
his  share  for  $1250.     What  was  the  total  value  of  the  business? 

6.  A  merchant  paid  $75  for  platform  scales,  which  was  62%% 
of  the  cost  of  his  wagon,  and  the  cost  of  the  wagon  was  75%   of 
the  cost  of  his  horse.     What  was  the  total  cost  of  his  chattels  ? 


PERCENTAGE  155 

7.  A  young  man  spends  25%  of  his  income  for  board,    15% 
for  clothes,   and  saves  45%.     The  remainder,   $225,   he  spends 
for  charity,  lodge  dues,  and  sundries.     What  is  his  total  income? 

8.  The  Surplus  Fund  of  a  bank  is  200%  of  its  Circulation  ;  its 
Circulation  is  50%  of  its  Capital  Stock,   and  its  Capital  Stock  is 
300%  of  the  Cash  on  Hand.     If  the  Surplus  Fund  is  $150000, 
what  is  the  Cash  on  Hand  ? 

9.  In  a  cask  of  vinegar  7  gallons  of  water  was  added.     This 
was  14^7%  of  the  total  contents.     How  many  gallons  of  pure 
vinegar  in  the  cask  at  first  ? 

10.  Hardin  lost  25%  of  his  stock  in  a  blizzard,  20%  of  the  re- 
mainder died  before  spring;  he  then  sold  33%%  of  the  remain- 
der, and  found  that  he  had  280  head  left.  How  many  did  he 
have  at  first  ? 


CASE  IV 

548.  Given,  the  Amount  or  Difference  and  the  Rate  to 
find  the  Base. 

Divide  the  amount  by  100%  plus  the  rate  to  find  the  base.      Di- 
vide the  difference  by  100%  minus  the  rate  to  find  the  base. 

FORMULA  :     Amount  7*-  100%  +  Rate  =  Base. 
Difference  -*-  100%  —  Rate  =  Base. 

549.  Solve  the  following  : 

1.  What  number  increased  by  10%  of  it  self  will  equal  88? 
By  12%%  of  it  self  will  equal  108? 

2.  What  amount  decreased  by  6%  of  itself  will  equal  $188  ? 
By  16%%  of  itself  will  equal  $300? 

3.  After  increasing  his  flock  of  sheep  33%%,  Jones  found  he 
had  728.     How  many  had  he  at  first? 

4.  John  lost  20%   of  his  marbles  on   Monday,   and   10%    of 
the  remainder  on  Tuesday,   when  he  had  54  remaining.     How 
many  had  he  at  first  ? 

5.  A  bookkeeper's  salary  was  increased  30%  of  90%  and  was 
then  $1016  per  year.     What  was  it  before  the  increase? 


156  MODERN    BUSINESS    ARITHMETIC 

6.  A  manufacturer's  profits  were  20%   less  the  second  year 
than  the  first ;  25%  less  the  third  year  than  the  second  when 
they  amounted  to  $8100.     What  were  the  profits  the  first  year? 

7.  Taylor  had  1008  acres  of  wheat  after  increasing  his  acre- 
age 20%  each  year  for  two  years.     How  many  acres  had  he  to 
begin  with  ? 

8.  An  assignee  paid  the  creditors  70  cents  on  the  dollar. 
What  was  A's  loss  if  he  received  $1330? 

9.  I  sold  a  piano  for  $425  and  gained  25%.     Had  I  paid  $50 
more  for  it  would  I  have  gained  or  lost,  and  how  much  ? 

10.  A  city's  population  increased  25%  the  first  year,  20%  the 
second  year,  33%  the  third,  40%  the  fourth,  and  50%  the  fifth, 
when  it  was  found  to  be  46200.  What  was  the  population  at 
the  beginning  of  the  first  year  ? 


HOME  WORK— No.  16 

1.  I  drew  out  33>i  %  of  the  $5220  I  had  in  the  bank ;  I  then 
drew  out  20%  of  the  remainder  ;  then  deposited  15%  of  what  I 
drew  out.     How  much  had  I  then  in  the  bank  ? 

2.  Twenty  per  cent,  of  A's  money  equals  30%   of  B's.     If 
they  together  have  $1250,  how  much  has  each? 

3.  I  sold  two  pieces  of  land,  each  for  $6480.     On  one  I  lost 
10%,  on  the  other  I  gained  12^ %.     Did  I  gain  or  lose  on  the 
whole  transaction,  and  how  much  ? 

4.  Brown  sold  his  automobile  for  $1980  which  was  10%   less 
than  his  asking  price,  and  his  asking  price  was  10%   more  than 
the  cost.     What  did  it  cost  him  ? 

5.  A,  B,  and  C  are  partners  in  business.     A  invests  tw7ice  as 
much  as  B,  and  B  invests  twice  as  much  as  C.     If  A's  gain  is 
20%  of  his  capital,  B's  25%  of  his,  and  C's  33/^%   of  his,   and 
their  total  gain  and  capital  together  is  $7770,  what  did  each  in- 
vest ? 


Profit  and  Loss 


550.  Profit  and  Loss  treats  of  the  gains  and  losses  in  bus- 
iness. 

551.  Gains  and  Losses  are  usually  estimated  at  a  certain 
rate  per  cent.,  therefore  the  principles  of  Percentage  apply  to 
this  subject. 

552.  The  Elements  of  Profit  and  Loss  are  :     The  Cost,  the 
Rate  of  Gain  or  Loss,  the  Gain  or  Loss,  and  the  Selling  Price. 

553.  The  Cost  is  the  base  of  percentage  and  represents  the 
investment. 

554.  The  Rate  is  the  profit  or  loss  per  cent. 

555.  The  Profit  or  1/OSS  is  the  percentage. 

556.  The  Selling  Price  is  the  amount  if  there  be  a  gain, 
or  difference  if  their  be  a  loss. 

557.  In  solving  the  problems  of  Profit  and  Loss,  note  the 
elements  given  and  apply  the  principles  of  Percentage. 


CASE  I 

558.  Given,  the  Cost  and  Rate  to  find  the  Gain  or  Loss. 
FORMULA  :     Cost  X  Rate  =  Gain  or  Loss. 

559.  Solve  the  following  : 

1 .  What  is  the  gain  on  a  piano  bought  for  $400  and  sold  at  a 
profit  of  25%? 

2.  Bought  potatoes  at  40  cents  per  bushel  and  sold  them  at 
371/2%  gain.     Find  the  profit. 

3.  Find  the  gain  on  goods  bought  for  $1500  and  sold  at  an 
advance  of  16%%. 

4.  I  bought  50  bales  of  hops,  averaging  175  Ibs.  to  the  bale, 
at  11  cents  per  lb.,  and  sold  them  at  a  profit  of  25%.     Find  my 
gain. 


158  MODERN    BUSINESS    ARITHMETIC 

5.  How  much  did  I  receive  for  goods  bought  for  $245  and 
sold  at  a  loss  of  15%  ? 

6.  I  bought  goods  for  $38.50,    paid  freight  $1.25,   drayage 
$.75,  and  sold  them  at  a  profit  of  33^3  % .     Find  the  selling  price. 

7.  Brown  bought  an  automobile  for  $1250;  he  then  sold  it 
to  Jones  and  gained  20%  ;  Jones  sold  it  to  Smith  at  a  profit  of 
25% .     What  did  Smith  pay  for  the  machine  ? 

8.  What  is  the  selling  price  of  a  car  bought  for  $2650  and 
sold  at  a  loss  of  10%  ? 

9.  Lambert  sold  40%  of  his  stock  of  produce  at  20%   gain; 
30%  at  15%  gain,  and  the  remainder  at  10%  loss.     If  his  total 
stock  cost  $420,  what  was  his  total  net  gain  ? 

10.  Bernardi  bought  goods  for  $16424.  He  sold  }i  of  them 
at  20%  profit,  YI  of  the  remainder  at  25%  profit,  YZ  of  those 
yet  remaining  at  12>^%  loss,  and  the  remainder  at  10%  gain. 
What  was  his  net  gain  ? 


CASE  II 

560.  Given,  the  Gain  or  1/oss  and  the   Cost  to  find  the 
Rate. 

FORMULA  :     Gain  or  L,oss  -5-  Cost  =  Rate. 

561.  Solve  the  following: 

1.  Goods  bought  for  $80  on  which  a  gain  of  $20  is  made  is  a 
gain  of  what  %  ? 

2.  If  the  cost  of  a  carriage  is  $120  and  it  is  sold  at  a  profit  of 
$30,  what  is  the  rate  of  gain  ? 

3.  I  made  a  profit  of  $72   on    a    piano    that    cost   me   $400. 
What  was  the  rate  of  profit  ? 

4.  Smith  sold  a  house  for  $2150  that  cost  him  $1500.     What 
was  his  gain  %  ? 

5.  If  wheat  selling  for  21  cents  per  bushel   more  than  cost 
brings  91  cents  per  bushel,  what  is  the  rate  of  gain  ? 


PROFIT  AND  LOSS  159 

6.  What  %  does  a  grocer  make  who  buys  sugar  at  4/4  cents 
per  Ib.  and  sells  it  at  5  cents  per  Ib.  ? 

7.  Wool  that  cost  28  cents  per  Ib.  was  damaged  and  then 
sold  for  21  cents  per  Ib.     What  was  the  rate  %  of  loss? 

8.  Find  the  average  rate  of  gain  on  the  following:     Calico 
bought  at  4  cents  and  sold  at  5  /4   cents ;  gingham  bought  at  8 
cents  and  sold  at  12%  cents;  silesia  bought  at  7  cents  and  sold 
at  10^  cents. 

9.  A  contractor  pays  his  men  $3.50  per  day  for  their  labor 
and  receives  $4.20  per  day.     What  %  of  profit  does  he  make? 

10.  My  salary  was  increased  20%  the  first  month;  25%  the 
second  month;  33/3%  the  third  month.  What  was  the  total 
rate  of  increase  ? 


CASE  III 

562.  Given,  the  Gain  or  I/oss  and  the  Rate  to  find  the 
Cost. 

FORMULA  :     Gain  or  Loss  -*-  Rate  =  Cost. 

563.  Solve  the  following  : 

1.  My  profit  was  $12.50  and  the  rate  of  gain  was  25%.     Find 
the  cost. 

2.  If  my  gain  was  18%,  or  $126,  what  was  the  cost  ? 

3.  I  lost  16^  by  selling  goods  $540  below  cost.     Find  the 
cost. 

4.  By  selling  hops  at  a  gain  of  $320,    I   made   16%.     I  in- 
vested the  proceeds  in  oranges  which  I   sold  at  a  loss  of  $40. 
For  what  did  I  sell  the  oranges  ? 

5.  Find  the  cost  of  goods  sold  at  $700  profit,   or  a  gain  of 
142/7%. 

6.  Lumber  sold  at  a  profit   of  $3.50  per  M.   is  a  gain  of 
17^2%.     Find  the  cost. 

7.  My  gain  for  the  month  is  $385.50,   or  20%   on  the  cost. 
What  was  the  cost  of  the  goods  sold  ? 


160  MODERN    BUSINESS    ARITHMETIC 

8.  A  and  B  each  gains  33/<3%  on  his  investment.     A's  gain 
is  $420,  and  B's  gain  is  $510.     How  much  more  had  B  invested 
than  A  ? 

9.  Brown's  gain  is  15%  of  his  investment;  Green's  is  22%% 
of  his.     If  they  each  gain  $900,  how  much  more  has  Brown  in- 
vested than  Green  ? 

10.  The  profits  of  a  bank  for  six  months  was  $16500,  or7l/4% 
on  the  Capital  Stock  and  Surplus.  If  the  Surplus  was  $120000, 
what  was  the  Capital  Stock  ? 


CASE  IV 

564.  Given,  the  Selling  Price  and  the  Rate  to  find  the 
Cost. 

FORMULA  :     Selling  Price  -=-  1  +  Rate  =  Cost ;  or, 
Selling  Price  •*•"!.—  Rate  =  Cost. 

565.  Solve  the  following  : 

1.  Find  the  cost  of  goods  sold  for  $27.50,   the  rate  of  gain 
being  10%. 

2.  Find  the  cost  of  a  piano  sold  at  a  loss  of  16^3  %  and  bring- 
ing $280. 

3.  Having  used  my  automobile  for  6  months,   I  sold  it  for 
$1000,  which  was  25%  below  cost.     What  did  it  cost? 

4.  I  sold  a  carriage  to  Smith  and  gained  \2%%  ;  Smith  sold 
it  to  Jones  for  $132  and  gained   10%.     What  did  the  carriage 
cost  me  ? 

5.  Some  city  lots  increased  in  value  each  year  25%   on  each 
previous  year's  value.     At  the  end  of  4  years  they  were  sold  for 
$3906.25.     What  did  they  cost  ? 

6.  At  what  price  shall  I  mark  goods  that  cost  me  $420  that  I 
may  give  a  10%  discount  and  still  make  a  20%  profit? 

7.  Flour  that  cqst  $3.60  per  bbl.  must  be  listed  at  what  price 
that  a  reduction  of  25%  may  be  made  and  still  leave  a  profit  of 

25%? 


PROFIT  AND  LOSS  161 

8.  I  sold  2  pianos,  each  for  $384  ;  on  one  I  gained  20%  ;  on 
the  other  I  lost  20%.     Did  I  gain  or  lose  on  the  whole  transac- 
tion, and  how  much? 

9.  Brown  sold  his  crop  of  grapes  at  a  profit  of  12/4%  on  the 
cost  of  raising.     Had  the  cost  been  $720  more,    he  would  have 
lost  12%  % .     For  what  did  he  sell  them  ? 

10.     If  I  buy  goods  at  25%  off  list  and  sell  them' at  20%  above, 
what  %  do  I  make  ? 


HOME  WORK— No.  17 

1.  I  buy  goods  at  50%  off  and  sell  at   25   and  10%    off  list 
price.     What  per  cent,  profit  do  I  make? 

2.  I  mark  goods  at  33//3%  above  cost.     If  I  allow  a  discount 
of  10%  from  the  marked  price,  what  per  cent,  profit  do  I  make? 

3.  I  sold  a  piano  at  a  loss  of  12%  %   and  lost  $80.     What 
would  I  have  gained  had  I  sold  it  at  a  profit  of  1824%  ? 

4.  Bought  oranges  which  I  sold  at  a  gain  of  16.^3%,   and  in- 
vested the  proceeds  in  eggs  which  I  sold  at  a  profit  of  10%.     If 
the  eggs  brought  $423.50,  what  did  the  oranges  cost? 

5.  Hanson's  sales  for  January  were  $5544.     What  was  his 
rate  of  gain  if  his  total  profits  were  $792  ? 

6.  At  what  price  shall  I  mark  goods  that  cost  $70  that  I  may 
discount  the  bill  12>^%  and  still  make  20%  ? 

7.  A  grocer  buys  goods  on  an  average  discount  of  20%   off 
list  price.     What  per  cent,  profit  does  he  make  if  he  sells  at  an 
average  of  10%  above  list  price? 

8.  A  dealer  sold  two  lots  of  land  at  $1012  each.     On  one  he 
made  a  profit  of  15%,  and  on  the  other  he  lost  12%.     Did  he 
gain  or  lose  on  both  transactions,  and  how  much  ? 

9.  A's  gain  of  20%  was  equal  to  B's  gain  of  30%.     If  their 
total  gain  amounted  to  $675,  what  was  the  capital  of  each  ? 

10.  By  selling  goods  at  a  certain  price  a  merchant  gained 
\62/3  % .  Had  the  goods  cost  him  $300  more  he  would  have  lost 
6//3  % .  What  was  the  cost  of  the  goods  ? 


Trade  and  Cash  Discounts 

566.  Trade  Discount  is  a  deduction  made  from  the  list 
price  of  an  article  to  fix  its  selling  price. 

567.  Cash  Discount  is  a  deduction  made  from  the  selling 
price  of  an  article  to  secure  cash  payment. 

568.  The  List  Price  is  an  established  price,    usually  pub- 
lished in  catalogues,   for  the  purpose  of  securing  a  basis  from 
which  trade  discounts  may  be  made. 

569.  The  Selling  Price  is  the  contract  price  for  which  the 
goods  are  sold  and  is  called  the  net  amount. 

570.  The  Terms  are  the  conditions  upon  which  a  bill  is 
sold  and  they  are  usually  printed,  stamped,  or  written  upon  the 
"bill   heads."     Thus,    "Terms,    60  ds.;    30  ds.,    5%;    10  ds. 
10%;  "  etc. 

571.  Legal  Interest  may  be  collected  on  all  bills  over  due, 
and  when  paid  before  maturity,  a  discount  is  usually  allowed. 

572.  A  Succession  of  Discounts  are  frequently  made. 
Thus,  20  and  10%  off  ==  100%  —  20%  =  80%.     10%   off  80% 

=  8%.     80%  —  8%  =  72%,  Ans. 

573.  Trade  and   Cash  Discounts  are  estimated    at  a  certain 
per  cent.,  therefore  the  principles  and  cases  of  Percentage  apply 
to  this  subject. 


CASE  I 

574.     Given,  the  List  Price  and  Rates  of  Discount  to 

find  the  net  amount  of  the  Bill. 

FORMULA  :     List  Price  X   100%  -  -  Rate   %   of  Discount  - 
Net  Amount  of  Bill. 


TRADE  AND  CASH  DISCOUNTS  163 

575.  If    a   succession  of  discounts  are  given,   treat  each  net 
amount  as  a  new  list  price  and  compute  the  discount  as  given  in 
the  above  formula. 

EXAMPLE  :     Find  the  net  amount  received  for  a  piano,  listed 
at  $800,  and  sold  for  25%  and  10%  off. 

100%  —  25%  ==  75%,         $800  X  75%  =  $600. 
100%  -  -  10%  =  90%.         $600  X  90%  ==  $540,  Ans. 

It  will  be  noticed  that  the  sum  of  25%   and   10%,    or  35%,   is 
not  the  same  as  25%  and  10%  off. 

576.  Solve  the  following  : 

1.  Find  the  net  amount  of  goods  listed  at  $500,  less  25%  dis- 
count. 

2.  List  price  $840,  less  12^2  %  discount. 

3.  List  price  $1250,  less  20  and  10%  discount. 

4.  List  price  $4320,  less  16^  and  25%  discount. 

5.  List  price  $1200,  less  33^i,  25,  and  10%  discount. 

6.  Find  the  net  amount  of  a  bill  for  a  carload  of  14  tons  of 
prunes,  listed  at  8  cents  per  lb.,   less  25  and  33>o%   discount. 

7.  Pianos  listed  at  $1200,  $1000,  $900,  $800,   and  $600  were 
were  discounted  33^i,  20,  and  10%  off.     Find  the  net  values  of 
each. 

8.  A  bill  of    clothing  which  amounted  to  $1420,    was  dis- 
counted 20  and  5%  off,  writh  an  additional  discount  of  2%   for 
cash.     What  amount  of  cash  would  pay  the  bill  ? 

9.  The  "terms"  of  a  bill  were  "60ds.,  5%  30  ds.,  10%    10 
ds."     If  the  total  amount  was  $720,  with  a  trade  discount  of  15 
and  10%,  what  amount  would  settle  the  bill  if  paid  in  8  days? 
In  20  days?     In  40  days? 

10.  Which  is  better  for  the  buyer,   50,   20,   and   10%   off,   or 
33^,  25,  and  25%  off,  and  how  much? 


164  MODERN    BUSINESS    ARITHMETIC 

CASE  II 

577.  Given,  the  Net  Amount  of  a  bill  and  the  Rate  of 
Discount  to  find  the  List  Price. 

FORMULA  :     Net  Amount   -*-   100%   -  -  Rate  of  Discount  — 
List  Price. 

578.  If  a  succession  of  discounts  are  made,  treat  each  list  price 
found  as  a  new  net  amount  and  proceed  as  per  formula. 

EXAMPLE  :     Find  the  list  price  of  a  piano  sold  for  $540,   the 
discounts  being  25  and  10%  off. 

100%  --  10%  =  90%.         $540  -4-  90%  =  $600. 
100%  —  25%  =  75%.         $600  -*-  75%  =  $800,  Ans. 

579.  Solve  the  following  : 

1.  Find  the  list  price  of  goods  sold  for  $315,   the  discount 
being  10%. 

2.  Selling  price  $551.25,  discount  25%. 

3.  Selling  price  $504,  discount  33^i  and  10%  off. 

4.  Selling  price  $612,  discount  20,  33/i.  and  10%  off. 

5.  Selling  price  $801,  discount  33M*,  25,  20,  and  10%  off. 

6.  Find  the  list  price  of  gloves  per  dozen,   which  retailed   at 
90  cents  per  pair,  a  discount  of  50  and  10%  being  allowed. 

7.  I  made  25%  on  goods  that  cost  me  $280,   by  selling  at  a 
discount  of  20%  from  marked  price.     Find  the  marked  price. 

8.  At  what  price  shall  I  mark  goods  that  cost  $208.80,  that  I 
may  discount  the  bill  40  and  20%  and  still  make  33/3  %  ? 

9.  Sewing  machines  were  sold  for  $45.60.     If  the  first  dis- 
count was  20%  and  the  total  discount  32%,  what  was  the  second 
discount  ? 

10.  Smith  &  Co.  buy  shoes  listed  at  $96  per  case  of  2  doz. 
each,  at  40  and  30%  off.  What  discount  in  addition  to  25% 
shall  they  make  in  order  to  sell  at  a  gain  of  50%  ? 


TRADE  AND  CASH  DISCOUNTS  165 

HOME  WORK-NO,  is 

1.  My  discount  on  a  piano  listed  at  $800  was  $160.     What 
was  the  rate  of  discount  ? 

2.  I  paid  $36  for  a  sewing  machine,  which  was  a  discount  of 
$9  from  the  list  price.     What  was  the  rate  of  discount  ? 

3.  Which  is  the  greater  rate  of  discount,    and   how  much, 
$24.30  off  $450,  or  $15.40  off  $280? 

4.  If  I  buy  goods  marked   at  $900,   at  33;^%   and  a  second 
rate  off,  for  $480,  what  is  the  second  rate  of  discount  ? 

5.  What  discount  is  equivalent  to  40,  33  >3,  and  20%  off. 

6.  Which  is  the  cheaper,  to  buy  goods  for  25,  33^,  and  10% 
off,  or  40,  20,  and  5%  off,  and  how  much  on  a  purchase  listed 

at  $400  ? 

7.  A  machine  listed  at  $360  was  discounted  20%  and  $14.40. 
What  was  the  second  rate  of  discount  and  the  selling  price  ? 

8.  Jones  paid  $512  for  goods  after  being  allowed  a  discount 
of  33:/3  and  20%  off.     What  was  the  marked  price? 

9.  Smith  received  a  discount  of  60,    25,    16^,    and   10%    on 
hardware  that  cost  him  $1575.     What  was  the  list  price? 

10.     I  sold  a  piano  for  35  and  25%   off  list  for  $585,   and  still 
made  17%  profit.     Find  the  cost  and  the  list  price. 


COMMISSION 

580.  Commission  is  a  compensation  charged  by  an  agent 
for  buying,  selling,  or  collectijig  for  another. 

581.  An  Agent  is  one  who  transacts  business  for  another. 

582.  A  Commission  Merchant  is  an  agent  whose  princi- 
pal business  is  to  buy  and  sell  goods  for  others  for  a  commission. 

583.  A  Principal  is  one  for  whom  an  agent  transacts  busi- 
ness. 

584.  A  Shipment  is  the  merchandise  sent  to  a  commission 
merchant  to  be  sold. 

585.  A    Consignment  is  the  merchandise  received  by  a 
commission  merchant  to  be  sold. 

NOTE— A  SHIPMENT  by  the  principal  is  a  CONSIGNMENT  to  the  agent. 

586.  The  Consignor  or  Shipper  is  the  one  who  sends  the 
goods. 

587.  The  Consignee  is  the  one  to  whom  the  goods  are 
sent. 

588.  Freight  and  Dray  age  are  the  charges  paid  to  the 
railway  and  transfer  companies  for  transportation. 

589.  Insurance  and  Storage  are  sometimes  charged  by  a 
commission  merchant  to  reimburse  him  for  sums  paid  on  general 
insurance  and  rent  accounts. 

590.  Guaranty  is  a  charge  to  insure  against  loss  through 
bad  debts.     It  is  generally  included  in  the  commission  charged. 

591.  A  Shipment  Invoice  is  a  list  of  goods  forwarded  to 
be  sold  on  commission. 

592.  An  Account  Sales  is  a  statement  rendered  by  a  com- 
mission merchant  to  the  consignor,  and  contains  : 

1.  A  list  of  goods  received  to  be  sold. 

2.  An  itemized  list  of  goods  sold. 

3.  The  charges  in  detail. 

4.  The  net  proceeds. 

5.  A  communication  stating  the  manner  of  remittance  or  of 
making  the  credit. 


COMMISSION  167 

593.  The  Total  Sales  is  the  sum  received  for  the  goods 
before  any  charges  are  deducted. 

594.  The  Net  Proceeds  is  the  sum  left  after  deducting  all 
charges. 

595.  An  Account  Purchase  is  an  itemized  statement  of 
goods  purchased  by  a  commission  merchant  togethei  with  freight, 
commission,  and  other  charges. 

596.  The  Entire  Cost  is  the  total  amount,   including  first 
cost  of  goods  and  all  charges. 

597.  Since  Commission  is  usually  computed  at  a  certain  rate 
per  cent.,  the  cases  of  percentage  may  apply. 

598.  The   Amount   of   Sale,   Purchase  or  Collection  is  the 
Base.     The  Rate  of  Commission  is  the  Rate.     The  Commission 
is  the  Percentage.     The  Entire  Cost  is  the  Amount,  and  the  Net 
Proceeds  is  the  Difference. 


CASE  I 

599.  Given,  the  Amount  of  Sale,  Purchase,  or  Collec- 
tion, and  the  Rate  of  Commission  to  find  the  Commission. 

(        Sale       ) 

FORMULA  :     Amount  of  j  Purchase  >  X  Rate  =  Commission. 

(  Collection  ; 

EXAMPLE  :  A  commission  merchant  sells  a  consignment  of 
eggs  for  $440,  and  charges  5%  commission.  What  is  his  com- 
mission ? 

$440  X  5%  =  $22,  commission. 

600.  Solve  the  following  : 

1.  What  is  the  commission  on  a  sale  of  $1200  at  3%  ? 

2.  On  a  purchase  of  goods  amounting  to  $4260  the  commis- 
sion charged  was  2\% .     Find  amount  of  commission. 

3.  My  agent  collected  bills  amounting  to  $575,  on  a  commis- 
sion of  10%.     What  is  his  commission,  and  what  amount  should 
I  receive? 

4.  My  agent  sold  52  bales  of  hops,  averaging  180  Ibs.    each, 
at  15  cents  per  lb.,  and  sent  me  a  draft  to  cover  the  sales  less  his 
commission  of  4%.     Find  face  of  the  draft. 


168 


MODERN    BUSINESS    ARITHMETIC 


5.  A  commission    merchant  was  instructed   to  purchase  20 
boxes  of  oranges  at  $2.75  each  ;   15  crates  of  bananas  at  $3  each; 
and  12  boxes  of  lemmons  at  $3.50  each.     Find  the  entire  cost, 
the  freight  charges  being  $2.25,  and  his  commsssion  6%. 

6.  An    agent  collected   the  following  bills:     J.   E.   Brown, 
$141.25;  I.  J.  King,  $78.40;  H.  C.  Hill,  $27.70;  R.  L.  Jones, 
$189.25;  T.  E.  Smith,  $52.50.     What  did  his  principal  receive 
if  he  paid  $2.60  expenses  and  12\%   commission   for  collecting? 

7.  L.  Ayers  directed  his  agent  to  purchase  $9000  worth  of 
prunes  and  to  ship  the  same  to  a  New  York  agent  who  sold  them 
for  $13520.     If  the  freight  charges  were  $300,   and  the  rate  of 
commission  for  buying  was  5  % ,  and  for  selling  4  % ,  what  did  he 
profit  by  the  transaction  ? 

8.  Find  the  net  proceeds  of  the  following  : 

Account  Sales 

B.  S.  TAYLOR  &  COMPANY 

COMMISSION  MERCHANTS 


Received  of  THE  MERRITT  FRUIT  PACKING  CO. , 

Santa  Rosa,  California 

To  be  sold  on  their  account  and  risk: 

400  boxes  Early  Crawford  Peaches 
100  Crates  Strawberries 


July 

200  Boxes  Peaches         Si.  40 

50  Crates  Strawberries     6.  — 

4uly 

3  200  Boxes  Peaches          1.25 

50  Crates  Strawberries     5.  — 

CHARGES  : 

July 

1 

Freight 

81 

25 

July 

3 

Cartage 
Commission,  10%  on  sales 

14 

73 

Net  Proceeds  remitted  in  cash 

COMMISSION 
9.     Find  the  entire  cost  of  the  following  : 


169 


Account  Purchase 


R.  J.  PERKINS  &  COMPANY 

COMMISSION  MERCHANTS 


I,os  Angeles,  Cal.,    July  28,    '08, 
Bought  for  KETTERLIN  BROS., 

Santa  Rosa,  California 

The  following  goods  per  their  order  of  July  25,   1908. 


PURCHASES  : 

50  Boxes  Navel  Oranges     S3.  25 
40   "    "     "         2.75 
35   "   Lemons            3.50 

CHARGES  : 

Freight 
Cartage 
Commission,  3% 

12 
3 

25 

50 

Amount  charged   -   - 

10.  A  commission  merchant  sells  7  tons  of  potatoes  at  1/4 
cents  per  lb.;  24  crates  of  cabbage,  120  Ibs.  each,  at  3  cents  per 
lb,;  270  bbls.  apples  at  $3.25  per  bbl.,  and  120  cases  of  eggs, 
36  doz.  to  the  case,  at  18^  cents  per  doz.  His  charges  are 
$23.50  for  cartage;  $5.80  for  storage;  >^%  for  insurance; 
1/4  %  for  guaranty  on  the  sale  of  apples  which  were  sold  on  ac- 
count, and  3%  for  his  commission.  What  were  the  net  pio- 
ceeds. 

CASE  II 

601.  Given,  the  Amount  of  Sale,  Purchase,  or  Col- 
lection and  the  Commission  to  find  the  Rate  of  Commission. 

Sale       ) 

FORMULA  :     Commission  H-  Amount  of      Purchase  \  =  Rate. 

Collection  ) 


170  MODERN    BUSINESS    ARITHMETIC 

EXAMPLE  :  The  commission  on  a  sale  of  cotton  amounting  to 
$6440  was  $225.40.  Find  the  rate  of  commission,  and  the  net 
net  proceeds. 

Com.  $225.40  H-  Amt.  of  Sale  $6440  =  3i%,  Rate. 
$6440  —  $225.40  =  $6214.60,  Net  proceeds. 

602.     Solve  the  following  : 

1.  Find  the  rate  of  commission  when  $24.60  is  charged  for 
selling  goods  amounting  to  $1230. 

2.  Find  the  rate  of  commission  when  $16.71  is  charged  for 
buying  $278.50  worth. 

3.  My  agent  sold  a  house  and  lot  for  $2850.     His  commis- 
sion was  $71.25.     Find  the  rate  charged. 

4.  A  lawyer  collected  a  bill  of  $324.40  and  charged    $40.55 
commission.     What  was  the  rate  for  collecting? 

5.  Find  the  rate  of  commission  charged  when  $2 3 5. 40  is  paid 
for  buying  26750  Ibs.  of  wool  at  32  cents  per  Ib. 

6.  If  a  commission  merchant  charged  \°/o  for  insurance,  2\% 
for   guaranty,    and   the   total   charges   on   sales  amounting   to 
$1475.50  were  $88.53,  what  was  the  rate  of  commission  ? 

7.  I  paid  my  Chicago  agent  $20.25  from  a  sale  of  $320  worth 
of  dried  fruit.     If  the  cartage  was  $4.25,   what  was  the  rate  of 
commission  ? 

8.  An  agent  sent  me  $1072.56  as  the  net  proceeds  of  a  total 
sale    amounting    to    $1117.25.     Find   the   rate   of   commission 
charged. 

9.  The  entire  cost  of  an  account  purchase  was  $968.30.     If 
the  incidental  charges  were  $9.20,   and  the  cost  of  the  goods 
bought  $920,  what  was  the  rate  of  commission  charged  ? 

10.  A  owed  B  $850.  Not  being  able  to  collect  the  bill,  B 
placed  it  in  the  hands  of  a  collector  who  succeeded  in  collecting 
80%  of  the  debt.  If  the  collector's  charges  were  $42,  including 
notary's  fee  of  $1.20,  what  was  the  rate  of  collection,  and  what 
was  B's  loss? 


COMMISSION  171 

CASE  III 

603.     Given,  the  Commission  and  the  Rate  of  Commis- 
sion to  find  the  Amount  of  Sales,  Purchase,  or   Collection. 

Sale 


FORMULA  :     Commission  -5-  Rate  =  Amount  of 


Purchase 


Collection. 

EXAMPLE  :     An  agent's  commission  was  $41.35  at  a  5%  rate. 
Find  the  amount  of  goods  sold. 

Com.,  $41.35  •*-  Rate,  5%  ~-=  Amt.  of  sale,  $827. 
604.     Solve  the  following  : 

1.  The   commission   is   $210;    the    rate    is   3%.     Find  the 
amount  of  goods  sold. 

2.  The  commission  is  $123.50;    the  rate  2}4%.     Find  the 
amount  of  purchase. 

3.  My  agent  collected  a  bill  charging  8%   commission.     If 
his  fee  amounted  to  $19.40,  how  much  did  I  receive? 

4.  My   agent's  commission  on  a  sale  was  $99.40;  the  rate 
charged  was  7  % .     What  was  the  amount  of  sale  ?— 

5.  A  commission  merchant  charged  a  commission    of  5%, 
guaranty  1%,   and  insurance  /4%.     If  his  total  charges  were 
$94.25,  what  was  the  amount  of  sale? 

6.  My  agent  charged  5%    for  selling  and  4%    for  buying. 
What  wrould  be  the  net  proceeds  of  a  sale,  and  the  entire  cost  of 
a  purchase  if  his  commissions  were  $135.25  and  $123.40  respect- 
ively ? 

7.  An  agent  collected  a  bill  on  a  commission  of  6%    and  re- 
mitted the  proceeds  less  his  commission  of  $38.40.     What  was 
the  amount  remitted  ? 

8.  A  collection  agent's  charges,   including  notary's  fees  of 
$2.75,  and  $1.50  for  recording,  were  $33.27  ;  his  rate  of  collec- 
tion was  4%.     What  amount  did  his  principal  receive? 

9.  A  commission  merchant  sold  a  consignment  of  cotton  at 
11  cents  per  Ib.  and  charged  a  commission  of  3/4%,  guaranty 
!>£%,  insurance  #%,  freight  $128.44,  and  cartage  $34.60.    If 
his  total  charges  amounted  to  $454.80,  how  many  pounds  of  cot- 
ton did  he  sell  ? 


172  MODERN    BUSINESS    ARITHMETIC 

10.  My  agent  sold  a  consignment  of  goods  at  33/^,  25,  and 
10%  off  list  price,  charging  me  6%  commission.  If  his  com- 
mission was  $76.95,  what  was  the  list  price? 


CASE  IV 

605.  Given,  the  Net  Proceeds  or  Entire  Cost  and  the 
Rate  of  Commission  to  find  the  Amount  of  Sale,   Purchase, 
or   Collection. 

FORMULA:  Net  Proceeds  -*-  100%  -  -  Rate  =  Amount  of 
Sale  or  Collection  ;  or,  Entire  Cost  -*-  100%  +  Rate  =  Amount 
of  Purchase. 

EXAMPLE  :  The  net  proceeds  of  a  sale  of  hams  and  bacon 
was  $695.52.  If  the  agents  commission  was  4%,  what  was  the 
value  of  the  goods  sold  ? 

Net  Proceeds,  $695.52  -*-  100%  —  Rate,  or  96%  =  Amt.  of 
Sale,  $724.50. 

606.  Solve  the  following  : 

.  1 .  I  received  $502 . 20  from  my  agent  as  the  net  proceeds  of  a 
sale.  His  commission  was  7  %.  Wnat  was  the  total  amount  of 
sale? 

2.  Smith  &  Co.,  directed  their  agent  to  purchase  lumber,  the 
entire  cost  of  which  was  $17757.20.     If  the  agent's  commission 
was  3  % ,  what  was  the  net  price  of  the  lumber  ? 

3.  The   Goodyear  Rubber  Company  received  a  New  York 
draft  for  $876.28  as  the  net  proceeds  of  a  collection  upon  which 
a  commission  of  5%    had   been   charged.     What   amount   was 
collected  ? 

4.  What  was  an  agent's  commission  at  6%   on  a  collection 
the  net  proceeds  of  which  were  $324.30  ? 

5.  Fairbank  &  Co.,   of  Chicago,  sent  their  N.   Y.   agent  a 
consignment  of  canned  goods  to  be  sold  on  a  2>^%  commission. 
The  net  proceeds,  after  paying  freight  $32.50,   drayage  $41.25, 
storage  $12.60,  and  the  commission,  was  $12159.65.     What  was 
the  amount  of  sale  ? 

6.  I  sent  my  St.  Louis  agent  a  car  load  of  oranges  to  be  sold 
on  a  commission  of  5%,  and  directed  him  to  invest  the  proceeds 


COMMISSION  173 

in  flour  after  deducting  his  commission  of  3%   for  buying.     If 
the  oranges  brought  $2140,  what  was  the  cost  of  the  flour? 

7.  A.  L.  Bagley  &  Co.  sent  their  agent  $930. 75  with  instruc- 
tions to  purchase  potatoes  after  deducting  his  commission  of  2%, 
and  to  sell  the  same  as  soon  as  the  market  price  advanced  10%. 
If  the  agent's  commission  for  selling  was  4%,  did  they  gain  or 
lose  by  the  transaction,  and  how  much  ? 

8.  Zimmerman  &  Co.  received  $402.33  as  the  net  proceeds  of 
a  sale  of  butter  after  deductions  were  made  as  fallows  :     Freight, 
$4.38;   cartage,  $1.25  ;    insurace,  ^  %  ;   guaranty,    2^4%  ;  and  a 
commission  of  3%.     How  many  pounds  of  butter  were  sold,   if 
the  price  paid  was  28  cents  per  pound  ? 

9.  A  commission  merchant  received  $49043.27,   and   was  di- 
rected to  invest  one-half  in  Island  cotton  at  12  cents  per  pound, 
the  remainder  he  invested   in  Southern  Alabama  cotton  at  10 
cents  per   pound,    after  deducting  2%    for  buying  each   kind. 
How  many  pounds  of  each  kind  of  cotton  did  he  purchase  ? 

10.  I  sent  a  commission  merchant  a  shipment  of  wine  and  di- 
rected him  to  sell  the  same  and  invest  the  proceeds  in  sugar 
after  deducting  his  commission  of  5%  for  selling  and  4%  for 
buying.  If  his  total  commission  was  $450,  what  was  the  selling 
price  of  the  wine,  and  the  cost  of  the  sugar? 


HOME  WORK— No.   19 

1.  A  commission  merchant  bought  goods  costing  $38450  on 
a  commission  of  2  % .     What  was  the  entire  cost  of  the  goods  ? 

2.  The  net  proceeds  of  a  sale,   after  deducting  $152.25  ex- 
pense and  a  commission  of  5%,  was  $6820.75.     \Vhatwasthe 
amount  of  the  sale  ? 

3.  A    commission   merchant   retained  $22.25  to  defray  the 
charges  for  selling  a  piano  for  $350.     If  the  cartage  was  $4.75, 
what  rate  of  commission  did  he  charge  ? 

4.  A  sale  of  $940  netted  me  $902.40  after  paying  insurance 
1%  and  a  commission.     What  was  the  rate  of  commission? 

5.  My  agent  remitted  me  $258  in  cash  after  paying  storage 
$11.40  and  retaining  his  commission   of  10%.     What  was  the 
amount  of  sale,  and  his  commission  ? 

6.  I  bought  goods  on  a  commission  of  6%.     If  the  entire 
cost  of  the  purchase  wras  $1847.05,  what  was  my  commission? 


174  MODERN  BUSINESS  ARITHMETIC 

7.  An  agent  sold  a  consignment  of  wool  for  $7210  and  was 
instructed  to  invest  the  proceeds  in  structural  steel,  after  deduct- 
ing his  commission  of  5%  for  selling  and  3%  for  buying.     What 
was  his  total  commission,  and  what  wras  the  price  paid  for  the 
steel  ? 

8.  I  sent  my  agent  $1440.40  in  cash  and  directed  him  to  in- 
vest in  flour,  after  deducting  his  commission  of  4%   for  buying. 
He  then  sold  the  flour  at  a  gain  of  20%  on  the  cost  price.    What 
was  his  rate  for  selling,    if  his  total  commission  amounted  to 
$138.50? 

9.  The  net  proceeds  of  a  sale  of  dried  fruits  consisting  of  8400 
Ibs.  of  prunes  sold  at  3i  cents,   4200   Ibs.    peaches  sold   at  4| 
cents,  and  12500  Ibs.  apples  sold  at  4  cents  per  Ib.  were  $905.40. 
If  the  charge  for  storage  was  $7.50,   and  for  insurance  $10.12, 
what  was  the  commission  and  rate  of  commission  ? 

10.  I  sent  my  agent  a  consignment  of  hops  to  be  sold  on  com- 
mission and  directed  him  to  invest  the  proceeds  in  wheat,  after 
deducting  7%  commission  for  selling  and  3%  for  buying.  If 
if  his  total  commission  was  $400,  what  was  the  selling  price  of 
the  hops,  and  the  cost  price  of  the  wheat  ? 


Outline  for  Review 

J.    Percentage :  III.     Trade  and  Cash 

1.  Definitions.  Discounts: 

2.  Classes  of  Subjects  :  1.  Definitions. 

First.  2.   List  Price. 

3.  Selling  Price. 

3.  bign.  ^    Terms    etc. 

4.  Kssential  Elements  :  c    r^ 

Base.  5-  Cases' 

£™unt-  IV.    Commission: 

Difference.  1-    Definitions: 

Percentage.  2.    Agent.      Principal. 

5.  Unit  of  Percentage.  3.  Commission  Merchant. 

6.  Cases.  4.  Shipment,  Consignment. 
-rr      T*     jz+        ^  T  5.  Consignor,  Consignee. 
II.     Profit  and  Loss:  6.  Freight,  Drayage. 

1.  Definitions.  7.   Insurance,   Storage,   Guar- 

2.  Elements:  anty. 

C°st^-  8.  Acct.  Sales,  Acct.  Purchase. 

Profit  or  Loss.  9.  Total  Sales,   Net  Proceeds, 

Selling  Price.  Entire  Cost. 

3.  Cases.  10.  Cases. 


Stocks  and  Bonds 

607.  A  Corporation  is  an  association  of  individuals  char- 
tered by  law  to  transact  business. 

608.  The  Articles  of  Incorporation  are  the  regulations 
governing  the  organization  of  the  association. 

609.  The  Articles  must  contain  the  following  : 

1.  The  name  of  the  corporation. 

2.  The  purpose  for  which  it  is  organized. 

3.  Its  principal  place  of  business. 

4.  The  term  of  its  existence. 

5.  The  number  and  names  of  the  directors. 

6.  The  amount  of  capital  stock  and  the  par  value  of  each 
share. 

7.  The  amount  of  capital  stock  actually  subscribed. 

610.  The   Capital  Stock  is  the  total  amount  of    all  the 
shares  that  may  be  issued  at  their  par  value. 

611.  Stocks  is  a  general  term  applied  to  shares  of  capital 
stock  of  all  kinds. 

612.  Stocks  are  at  par  when  they  sell  for  their  face  value ; 
above  par  when  they  sell  for  more,  and  below  par  when  they  sell 
for  less  than  their  face  value. 

613.  Certificates  of  Stock  are  issued  by  the  officers  of 
the  corporation  to  these  who  contribute  to  the  capital  stock,  and 
are  usually  transferable. 

614.  The  Market  Value  of  stock  is  the  amount  for  which 
it  can  be  sold. 

615.  Premium  and  Discount  are  terms  used  to  indicate 
the  difference  between  the  par  value  and  the  market  value. 

616.  Brokerage  is  the  percentage  charged  by  a  broker  for 
buying  or  selling  stocks.     It  is  usually  %%  or  }&%  on  the  par 
value  of  the  stocks. 


176  MODERN    BUSINESS    ARITHMETIC 

617.  A  Stock  Broker  is  one  who  buys  and  sells  stocks. 

618.  An  Installment  is  a  portion  of  the  capital  stock  paid 
in  by  the  subscribers. 

619.  An  Assessment  is  a  sum  required  of  the  stockholders 
to  meet  current  losses  or  needs  of  the  company. 

620.  A  Dividend  is  a.  percentage  paid  to  the  stockholders 
from  the  profits  of  the  business. 

621.  Bonds   are   the   promissory  notes  of   a  government, 
state,  municipality,  or  corporation. 

622.  Stock  Quotations  are  the  published  prices  for  which 
stocks  are  selling. 

623.  Bonds  like  Stocks  may  sell  at  a  premium  or  at  a  discount. 

624.  Bonds  are  of  two  kinds,  Registered  and   Coupon. 

625.  Registered  Bonds  are  those  payable  to  the  owner 
as  registered  on  the  books  of  the  company. 

626.  Coupon  Bonds  have  certificates  of  interest  attached, 
which  when  due  may  be  cut  off  and  presented  for  payment. 

627.  Treasury  Stock  is  that  portion  cf  the  Capital  Stock 
which  has  not  been  subscribed.     It  is  usually  reserved  for  the 
future  needs  of  the  corporation  and  may  be  sold  to  increase  its 
working  capital, 

628.  Preferred  Stock  is  stock  issued  usually  to  rehabili- 
tate a  corporation  in  a  weakened  condition,  and  takes  precedence 
in  the  matter  of  drawing  dividends.     Thus,  preferred  stock  may 
receive  a  certain  per  cent,  dividend  from  the  profits  cf  a  business 
and  the  remainder,  if  any,  may  be  distributed  as  dividends  on 
the  common  stock. 

629.  Watered  Stock  is  stock  issued  for  which  no  con- 
sideration is  received.     The  issuing  of  watered  stock  is  usually 
for  the  purpose  of  either  inflating  the  value  of  the  stock  of   a 
corporation  or  for  reducing  the  high  rate  per  cent,  of  profit  which 
in  some  states  is  forbidden  by  law. 

630.  Bonds  are  sometimes  designated  by  the  rate  of  interest 
they  bear.      As  "  Missouri  5's  "  =  Missouri  bonds  drawing  5%. 


STOCKS  AND  BONDS  177 

631.  Since  the  Premium,  Discount,  and  Brokerage  are  esti- 
mated at  a  certain  rate  per  cent.,  the  cases  of  Percentage  apply 
to  the  subject  of  Stocks  and  Bonds. 

632.  The  Quantities  considered  in  Stocks  and  Bonds  are ; 
Par  Value  =  Base ;  Rate  of  Premium,   Discount,  Dividend,  or 
Brokerage  =  Rate;  Premium,  Discount,  Dividend,  Assessment, 
or  Brokerage  =  Percentage  ;   Market  Value  =  Amount  or  Dif- 
ference. 

NOTE — The  par  value  of  the  stock  in  the  following:  problems  is  $100, 
and  the  rate  of  brokerage  is  \  per  cent,  unless  otherwise  specified. 
Brokerage  is  always  estimated  on  the  par  value. 


CASE  I 

633.  Given,  the  Par  Value  of  the  Stocks  and  the  Rate 

to  find  the  Premium,  Discount,  Dividend,  Assessment  or  Broker- 
age. 

(  Premium  or  Discount 
FORMULA  :     Par  Value  X  Rate  =    <  Dividend  or  Assessment 

(  Brokerage. 

EXAMPLE:     I  sold  44  shares  of  S.  P.  R.  R.  stocks  at  12% 
premium.     How  much  was  the  premium  ? 

44  shares  at  $100  each  =  $4400. 
$4400  X  12%  —  $528. 

634.  Solve  the  following  : 

1.  What  wras  a  broker's  commission  on  120  shares  of  N.  Y. 
Central's  sold  at  5%  discount? 

2.  Chicago  and  Rock  Island  shares  are  selling  at  8%  discount. 
What  is  my  broker's  commission  on  82  shares  sold  at  that  price? 

3.  I   received  an  8%  dividend  on   128  shares    of    B.   &  O. 
stock.     How  much  cash  did  I  receive  ? 

4.  My  profit  on  a  sale  of  32  shares  of  Union  Pacific's  was 
l2l/2%  less  brokerage.     What  was  my  gain? 

5.  A  bank  whose  capital  stock  is  $150000  declares  a  dividend 
of  3%.     What  is  the  total  dividend,  a*nd  how  much  does  Jones 
receive  who  owns  25  shares  ? 


178  MODERN    BUSINESS    ARITHMETIC 

6.  Lake  Shore  stocks  are  selling  for  $1071/£.     What  would 
be  the  premium  on  46  shares  ? 

7.  Amalgamated    Copper    is    12%  below    par.     How  much 
would  I  receive  for  96  shares  after  paying  brokerage  ? 

8.  Anaconda  Copper  Co.'s  stocks   ($50)    are  paying  a  2% 
quarterly  dividend.     What  annual  income  should  Green  receive 
who  owns  77  shares  ? 

9.  I  buy  140  shares  of  Canadian  Pacific's  at  167 X  and  sell  the 
same  at  171%,  paying  brokerage  both  for  buying  and  selling. 
What  is  my  profit  ? 

10.  Goldfield  Consolidated  levied  an  assessment  of  5%  upon 
its  stock  ($50)  for  development  purposes,  2%  for  current  ex- 
penses, and  4%  for  machinery.  What  would  be  the  total  assess- 
ment on  1000  shares,  and  how  much  would  be  required  of  A 
who  owns  45  shares  ? 


CASE  II 

635.  Other   Quantities  being  given  to  find  the  Rate  of 
Premium,  Discount,  Dividend,  Assessment  or  Brokerage. 

FORMULA:     Prem.,  Dis.,.Div.,  Ass.,  or  Brok.  -*-  Par  Val.  = 
Rate. 

EXAMPLE  :     A  dividend  of  $128  was  received  as  a  dividend  on 
64  shares  of  Bank  Stock.     What  was  the  rate  ? 

.Div..  $128  -H  Par  Val.,  $6400  =  2%  Rate. 

636.  Solve  the  following  : 

1.  The  par  value  of  stocks  is  $800;    the  dividend   is  $60. 
What  is  the  rate  of  dividend  ? 

2.  Par  value,  $1200  ;  dividend,  $132.     Find  the  rate. 

3.  Brokerage,    $14.50;    par  value,   $5800.     Find  the  rate  of 
brokerage. 

4.  I  sold  42  shares  of  Bait.   &   Ohio  at  a  discount  of  $189. 
What  was  the  rate  of  discount  ? 

5.  A  broker's  commission  is  $3.50.     What  rate  does  he  charge 
if  the  sale  is  56  (  $50  )  shares  ? 


STOCKS  AND  BONDS  179 

6.  Stock  received  at  par  was  sold  at  a  net  gain  of  $608.     If 
76  shares  were  sold  and  brokerage  charged,  what  was  the  rate  of 
premium? 

7.  An  electric  power  company  with  a  capital  of  $500000  has 
gross  earnings  amounting  to  $82000,  and  its  total  expenses  are 
$43250.     What  whole  rate  of  dividend  may  it  declare,  and  what 
surplus  would  remain  ? 

8.  The  net  earnings  of  the  Bullfrog  Mining  company  for  the 
year  were  $275000.     The  capital  stock  consists  of  5000  shares  of 
preferred   stock,    guaranteed  4%   semi  annual  dividends,    and 
10000  shares  of  common  stock.    What  annual  rate  of  dividend  can 
be  declared  on  the  whole  stock  after  paying  preferred  stock  divi- 
dends ? 

9.  A  National  bank  with  a  capital  of  $150000  has  net  earn- 
ings of  $21345.20.     If  10%  of  this  is  placed  in  a  reserve  fund, 
what  is  the  greatest  whole  per  cent,  of  dividend  that  it  may  de- 
clare, and  what  will  be  the  remaining  undivided  profits  ? 

10.  A  gas  company  is  able  to  declare  a  dividend  of  18%  on 
its  capital  stock  of  $200000.  If  it  waters  its  stock  by  the  addi- 
tion of  3000  shares,  what  rate  of  dividend  may  it  declare  on  the 
same  income  and  still  place  $1000  in  the  reserve  fund  ? 


CASE  III 

637.  Other  Quantities  being  given  to  find  the  Par  Value, 
Market  Value  >  or  the  Rate  of  Investment. 

FORMULA  :  Prem.,  Dis.,  Div.,  Ass.,  or  Brok.,  -s-  Rate  =  Par 
Value. 

Par  Val.  X  100%  +  Rate  =  Market  Value. 

Div.  -*-  Market  Val.  =  Rate  of  Investment. 

EXAMPLE  :  Stocks  sold  at  a  premium  of  $135  yields  a  prem- 
ium of  9% .  What  is  the  par  value  of  the  stocks  ? 

Prem.,  $135  -*•  Rate,  9%  =  $1500,  'Par  Val. 

EXAMPLE  :  The  par  value  of  electric  railway  stock  is  $4500  ; 
the  rate  of  discount  is  10%.  Find  the  market  value. 

Par  Val.,  $4500  X  90%  =  $4050,  Market  Value. 


ISO  MODERN    BUSINESS    ARITHMETIC 

EXAMPLE:     School  bonds  bought  at  120  yield  6%    interest. 
What  is  the  rate  of  income  ? 

Div.,  $6  •*-  Market  Val.,  $120  =  5%,  Rate  of  Investment. 
638.     Solve  the  following  : 

1.  Brown  receives  a  3%  semi  annual  dividend  of  $480.     How 
many  (  $50  )  shares  does  he  own  ? 

2.  What  will  be  the  cost  of  270  shares  of  N.  Y.  Central  Ry. 
stock  at  11 024  ;  brokerage  /8%  ? 

3.  My  broker  sold  115  shares  of  Southern  Pacific's  at   77l/2 
charging  brokerage  at  1/i%.     What  did  I  receive  for  my  stock? 

4.  I  invested  $5120  in  Northern  Pacific's    at   127  &,   paying 
brokerage.     If  a  dividend  of  8%   is  declared,   what  rate  of  in- 
vestment do  I  receive  ? 

5.  How  many  shares  of  stock  bought  at  IIO1/^  and  sold  at 
116%,    brokerage    1A%    for   buying    and  V±%   for  selling,   will 
gain  $690  ? 

6.  What  amount  must  be  invested  in  (  $50  )  stock  at  $62.50 
per  share,  paying  brokerage  /^%,   to  yield  an  income  of  $720, 
the  stock  paying  12%  dividend? 

7.  Which  is  the  better  investment,  Union  Pacific  5's  at  110 
or  Rock  Island  6's  at  120,  and  how  much  on  an  investment  of 
$39600  ? 

8.  I  directed  my  agent  to  sell  200  shares  of  preferred  ?tock 
at  97%,  yielding  3%  semi-annual  dividends,  and  directed  him  to 
buy  Edison  Electric's  at  208  which  yield  15%  annually.     Did  I 
increase  or  diminish  my  income,  and  how  much,  and  what  sur- 
plus was  left,  paying  brokerage  both  ways? 

9.  Glenn  &  Co.  sold  through  a  broker  500  shares  of  United 
Fruit  (  $100  )  stock  at  107,  paying  annual  dividends  of  6%,  and 
directed  him  to  invest  the  proceeds  in  U.  S.   Rubber  ($50)  at 
35%  and  paying  2  %  semi-annual  dividends.    Did  they  increase  or 
decrease  their  income  and  how   much,   and  what  surplus   was 
left ;  brokerage  /^  %  both  for  selling  and  buying  ? 


STOCKS  AND  BONDS  181 

10.  J.  A.  McDonald  &  Co.,  through  their  broker,  invested  a 
sum  of  money  in  Mich.  6's  at  109^,  and  twice  as  much  in  Ohio 
5's  at  98 3/i  I  brokerage  in  each  case  %%.  The  annual  income 
from  both  investments  was  $2772.  How  much  did  they  invest 
in  each  kind  of  stock  ? 


HOME  WORK—  No.  20 

1.  The  Western  Railway  Company  with  a  capital  stock  of 
$500000  declares  a  2%   quarterly  dividend.     What  will  be  A's 
annual  income  on  420  shares  ? 

2.  A   mining  company  with  a  capital   of  $250000  has    net 
earnings  amounting  to  $14275.     What  is  the  highest  whole  rate 
per  cent,  of  dividend  that  may  be  declared,   and  what  surplus 
would  remain  ? 

3.  What  per  cent,  of  income  does  stock  paying  6%  dividend 
yield  when  bought  at  120  ? 

4.  What  will  be  the  cost  of  240  shares  of  the  Wright  Bros. 
Aerial  Navigating  Company  quoted  at  84  X  ;  brokerage  X%  ? 

5.  My  broker  bought  320  shares  of  S.  P.  ($50)  stock  at  62% 
which  yielded  a  semi-annual  dividend  of  2%%.     What  was  my 
annual  rate  of  income  on  my  investment  ;  brokerage 


6.  I  directed  my  broker  to  sell  80  shares  of  Ohio  6's  at 

and  to  buy  Pennsylvania  5's  at  79^.     Did  I  increase  or  dimin- 
ish my  income,  and  how  much  ?     What  was  the  surplus  ? 

7.  What  price  must  be  paid  for  stocks  paying  4%   dividends 
to  yield  5%  on  the  investment? 


8.  Which  is  the  better  investment,   stocks  bought  at 

and  paying  5%,   or  stocks  bought  at  88  paying  4%,   and  how 
much  on  an  investment  of  $19800  ? 

9.  My  income  from  an  investment  in  Wabash  ($50)   6's  was 
$114.     If  I  paid  66%  and  brokerage  V±%  ,   what  amount  did  I 
invest  ? 

10.  I  sold  through  my  broker  54  shares  in  Consolidated  Vir- 
ginia ($100)  stock  at  148^  paying  3%  quarterly  dividend, 
and  directed  him  to  purchase  Bakersfield  Oil  Stock  (  $50  )  at 
94^  paying  8%  semi-annual  dividends.  Did  I  increase  or  de- 
crease my  income  ;  how  much,  and  what  was  the  surplus  ;  brok- 
erage X  %  ? 


TAXES 

639.  A  Tax:  is  a  certain  sum  levied  on  the  person,  property, 
or  income  of  a  person,   firm,   or  corporation  for  the  purpose  of 
defraying  the  expenses  of  the  government. 

640.  Property  Tax  is  a  tax  on  property.     Property  is  of 
two  kinds,  Real  Estate  or  Personal  Property. 

641.  A  Poll  Tax  is  a  tax  on   every  male  citizen  of  the 
State. 

642.  Real  Estate  is  land  and  permanent  improvements 
thereon. 

643.  Personal  Property  consists  of  all  kinds  of  movable 
property,  called  chattels. 

644.  An  Assessor  is  the  person  who  prepares  the  assess- 
ment rolls  and  estimates  the  values  of  property. 

645.  The  Tax  Collector  receives  the  taxes  and  gives  re- 
ceipts for  the  same. 

646.  Collection  is  a  sum  paid  to  a  collector  for  collecting 
taxes. 

647.  The  Assessment  Roll  is  the  list  of  the  taxable  prop- 
erty together  with  its  assessed  valuation. 

648.  Taxes    are  levied   for  different  purposes ;   as,   county, 
state,  school,  library,  street,  highways,  etc. 

649.  Since  taxes  are  estimated  as  a  certain  per  cent,   of  the 
assessed  value  of  the  property,  the  cases  of  Percentage  may  ap- 
ply. 

650.  To  find  the  Tax,  Rate  of  Taxation,  and  Assessed  Value 
of  taxable  property. 

FORMULA  :  Assessed  Value  X  Rate  =-  Tax. 
Tax  -r-  Rate  =  Assessed  Value. 
Tax  -£  Assessed  Value  =  Rate. 


TAXES  183 

651.     Solve  the  following  : 

1.  The  assessed  valuation  of  the  city  of  Santa  Rosa,   Cal.,    is 
$6,000,000,  and  the  rate  of  taxation  for  state  and  county  pur- 
poses is   1.42%,   and  for  municipal  purposes  1.25%.     What  is 
the  total  tax  ? 

2.  If  a  collection  fee  is  1%,  how  much  must  be  the  total  tax 
in  order  to  raise  sufficient  funds  to  build  a  courthouse  to  cost 
$321750? 

3.  A  tax  on  a  store  building  assessed  at  $27500  was  $68.75. 
At  the  same  rate,  what  would  be  the  value  of  another  building 
taxed  for  $92  ? 

4.  The  assessed  value  of  the  property  of  a  town  is  $1420000. 
The  total  tax  to  be  raised  is  $31950.     What  would  be  A's  tax 
who  is  assessed  for  $8400  ? 

5.  What  is  Brown's  tax  in  a  city  whose  rates  are  as  follows  : 
1%  for  improvements,  5  mills  on  the  dollar  for  library,   75  cents 
on  the  $100  for  county  tax,  14  mills  on  the  dollar  for  State  tax,  if 
he  is  assessed  at  $1200  and  one  poll  at  $2  ? 

6.  How  much  will  be  a  person's  tax  who  has  property  as- 
sessed for  $10540,  if  he  pays  1^4%  city  tax,    .54%   State  tax,   2 
mills  on  the  dollar  school  tax  ? 

7.  A  special  tax  was  levied  on  a  town  for  the  purpose  of 
building  a  bridge  the  net  cost  of  which  was  to  be  $1370.85.     If 
the  collector's  commission  was  2M}%  and  the  rate  of  taxation  2l/2 
mills  on  the  dollar,  what  was  the  assessed  valuation  of  the  town? 

8.  The  assessor's  roll  footed  up  $17235850.     The  expenses  of 
the  county  for  roads  was  7  mills  on  the  dollar ;  for  salaries,   4 
mills  on  the  dollar ;   for  jail,   county  farm,   and  other  charities, 
ll/2  mills  on  the  dollar ;   for  schools,   25  cents  on  the  $100 ;  for 
state  tax,  60  cents  on  the  $100.     If  there  are  12000  polls  at  $2 
each,  what  is  the  entire  tax  of  the  county  ? 

9.  What  is  my  total  tax  if  the  assessed  value  of  my  property 
is  $7200  and  the  rates  are  as  follows  :     Schools,  4  mills ;  general 
purposes,   5  mills ;  library,   .5  of  a  mill;    state  tax,   3.5  mills; 
hospital,  1  mill;  other  expenses,   3  mills;  and  I  pay  road  tax 
and  poll  tax  $2  each  ? 


U.  S.  Customs  or  Duties 

652.  Customs  or  Duties  are  taxes  levied  upon  imported 
goods  for  the  purpose  of  raising  funds  for  the  government  and  to 
protect  home  industries. 

653.  A  Custom  House  is  the  place  where  duties  are  col- 
lected . 

654.  A  Port  of  Entry  is  the  city  in  which  a  custom  house 
is  located. 

655.  The  Collector  of  the  Port  is  the  officer  who  col- 
lects duties  for  the  government. 

656.  A  Manifest  is  a  statement  in  detail  of  a  ship's  cargo. 

657.  A  Clearance  is  the  certificate  given  by  the  collector 
of  port  that  a  vessel  has  complied  with  the  requirements  of  law 
and  is  allowed  to  depart. 

658.  A  Tariff  is  a  schedule  of  the  rates  of  duty   required 
by  law  to  be  paid  en  imported  goods. 

659.  Ad  Valorem  Duty  is  the  duty  estimated  upon  the 
entire  cost  of  the  goods  in  the  country  from  which  they  are  ex- 
ported. 

660.  Specific  Duty  is  the  duty  estimated  upon  the  weight 
or  quantity  of  the  goods  imported  without  regard  to  their  value. 

661.  Allowances  are  made  for  the  tare,   leakage,  breakage, 
etc.,  before  the  duties  are  computed. 

662.  Tare  is  an  allowance  made  for  the  box,  crate,   or  cov- 
ering containing  the  goods. 

663.  Leakage  is  an  allowance  made  for  waste  of  liquids 
imported  in  casks,  barrels,  etc. 

664.  Breakage  is  an  allowance  made  en  account  of  waste 
of  goods  shipped  in  glass  or  other  breakable  material. 

665.  Gross  Weight  or  Gross  Value  is  the  entire  weight 
cr  value  before  any  deductions  are  made. 


UNITED  STATES  CUSTOMS  OR  DUTIES  185 

666.  Net  Weight  or  Net  Value  is  the  weight  or  value 
after  all  deductions  are  made. 

667.  Since  duties  are  estimated   at  a  certain  rate  per  cent., 
the  cases  of  Percentage  will  apply. 

668.  To  find  the  Duty,  Rate  of  Duty,  or  Value  of  Goods  im- 
ported. 

FOMUL,£  :  Net  Value  X  Rate  =  Duty. 
Duty  -8-  Rate  =  Net  Value. 
Duty  -*-  Net  Value  =  Rate. 

EXAMPLE  :  What  is  duty  on  540  yds.  cf  silk,  invoiced  at  3 
francs  per  yd.;  boxing  and  cartage,  5  francs;  the  specific  duty 
being  \2\  cents  per  yd.,  and  the  ad  valorem  duty  33| %  ? 

540  yds.  X  3  fr.  ==  1620  fr. 

1620  fr.  +  5  fr.  =  1625  fr.,  total  invoice  cost. 

1625  fr.  X  19.3  cents  =  $313.63. 

$314  X  33i%  =  $104.67,   ad  valorem  duty. 

540  yds.  X  12|  cents  =  $67.50,  specific  duty. 

$104.67  +  $67.50  =  $172.17,  total  duty. 

NOTE — The  LONG  TON  of  2240  Ibs.  is  used  in  weighing  goods  at  the 
custom  house. 

The  VALUE  of  the  £  is  $4.8665,     The  franc,  $.193.     The  mark,  $.2385. 

'  A  BONDED  WAREHOUSE  is  a  place  where  goods  on  which  duty  has  not 
yet  been  paid  may  be  stored. 

Duties  are  computed  on  WHOLE  DOLLARS  only.  If  the  fraction  is  50 
cents  or  more,  it  is  counted  as  a  whole  dollar ;  if  less  than  50  cents,  it  is 
dropped. 

PRACTICAL  PROBLEMS 

669.  Solve  the  following  : 

1.  What  is' the  duty  on  720  yds.  of  carpet  invoiced  at   10  s. 
6  d.  per  yd.,  the  duty  being  25%  ? 

2.  Find  the  specific  duty  on  38080  Ibs.  of  tool  steel  at  $58.50 
per  ton. 

3.  What  is  the  entire  duty  on  an  invoice  of  40  doz.   pairs  of 
kid  gloves,  costing  1420  francs  ;  boxing  and  cartage,  30  francs  ; 
specific  duty,  $1.80  per  doz.  pairs,  and  ad  valorem  duty,   20%  ? 


^86  MODERN    BUSINESS    ARITHMETIC 

4.  An   invoice  of   goods  from  Germany  was  billed  at  7240 
marks.     What  was  the  duty  at  35%  ? 

5.  Find  the  duty  on  13200  yds.  of  China  silk,  imported  from 
Shanghai,  invoiced  at  2  s.  6  d.  per  yd.     Ad  valorem  duty  16l%, 
and  specific  duty  8  cents  per  yd. 

6.  A  merchant  imported  240  pieces  of  carpet,  each  piece  con- 
taining 96  yds.,  invoiced  at  2/^  marks  per  yd.     The  ad  valorem 
duty  was  12/^%,  and  the  specific  duty  8^i  cents  per  yd.     What 
was  the  entire  cost  of  the  carpet  ? 

7.  What  is  the  rate  of  duty  on  an  invoice  of  goods,   the  en- 
tire cost -of  which  was  $1095.35,   including  boxing  and  cartage 
$22.50.  and  an  ad  valorem  duty  of  $182.60? 

8.  A  New  York  jobber  imported  from  England  10  cases  of 
English  broadcloth  ;  gross  weight,  1240  Ibs.;  value  ^550.     What 
was  the  cost  of  the  cloth  after  being  allowed  5%  tare  on  weight, 
the  duties  charged  being  40  cents  per  lb.,   and  37^%   ad  val- 
orem? 

9.  A  wine  merchant  imported  200  doz.  bottles  of  champagne 
invoiced  at  $15  per  doz.,  and  20  casks  of  port  wine,   each  con- 
taining 30  gals.,  invoiced  at  $2.25  per  gal.     A  breakage  of  10% 
and  a  leakage  of  20%  is  allowed  by  the  custom  officers.     What 
is  the  duty  at  33 /^%  ad  valorem  on   the  champagne,    and   20% 
on  the  port  ? 

10.  I  imported  two  kinds  of  watches  ;  on  the  first  I  paid  a 
duty  of  33>i%,  on  the  second  35%.  Including  duty,  I  invested 
twice  as  much  in  the  second  kind  as  in  the  first.  If  the  total 
duty  paid  wyas  $1660,  what  was  the  total  cost  of  each  kind  ? 


TAXES  AND  DUTIES  187 

HOME  WORK—  21 

1.  The  assessed  value  of  a  town  is  $4750000,  and  the  rate  of 
taxation  is  as  follows:     General  purposes,   80  mills;  hospital, 
4  mills  ;  school,  24  mills  ;  road,  27  mills,   and  library,    10  mills 
on  the  $100.     Find  the  total  tax. 

2.  My  total  rate  of  taxation  was  2^.  cents  on  the  dollar,  and 
my  tax  amounted  to  $229.35.     What  was  the  assessed  value  of 
my  property  ? 

3.  The  county  rate  of  taxation  was  $1.25,  the  state  rate  $.45. 
What  was  the  school  rate  if  my  tax  was  $192  on  an  assessed  val- 
uation of  $9600  ? 

4.  A  village  school  house  to  cost  $3981.25  was  paid  for  by  a 
tax  of  lX  cents  on  the  dollar.     If  the  collector's  commission 
was  2  %  ,  what  was  the  assessed  value  of  the  property  ? 

5.  The  assessed  value  of  the  property  of  a  town  is  $4,552,800. 
If  there  are  1145  polls  at  $2  each  and  a  collector's  fee  of  1%, 
what  rate  of  taxation  will  be  required  to  meet  a  net  expenditure 
of  $77392.26? 

6.  What  is  the  duty  on  imported  goods  invoiced  at  3240 
francs,  the  rate  of  duty  being  42%  ? 

7.  A  firm  imported  4800  yds.    of  body  brussels  carpet  in- 
voiced at  5  marks  per  yard,  a  charge  of  45  marks  for  boxing  and 
cartage   being  added    to   the  bill.     What  is  the  total  duty  at 

ad  valorem,  and  15  cents  per  yard  specific? 


8.  What  will  be  the  total  cost  of  an  invoice  of  watches,   im- 
ported from  London,   and  billed  at  ^584  15s.  6d.,   the  rate  of 
duty  being  35%,  exchange  being  $4.88? 

9.  A  paper  company  imported  from  Canada  500  long  tons  of 
wood  pulp  invoiced  at  1^4  cents  per  Ib.     What  was  the  entire 
cost,  if  the  boxing  and  cartage  was  $1.37^   per  ton;  freight, 
$1250,   paid  in  Holyoke,   Mass.  ;  specific  duty,  $2.25  per  ton, 
and  an  ad  valorem  duty  of  20%  ? 

10.  Hall  &  Co  imported  merchandise  billed  at  4320  marks,  on 
which  there  were  prepaid  charges  of  150  marks.  The  gross 
weight  was  7  tons,  on  which  a  tare  of  20%  was  allowed.  If  the 
specific  duty  was  $1.75  per  ton,  and  the  advalorem  duty  25%, 
what  was  the  entire  cost  of  the  goods  ? 


INSURANCE 

670.  Insurance   is   indemnity    against    loss.     There    are 
many  kinds  of  insurance,   and  they  take  their  names  from  the 
nature  of   their  risks  ;     as,    Fire  Insurance,  Marine  Insurance, 
Life  Insurance,  Accident  Insurance,  Health  Insurance. 

NOTE — Among  the  many  special  forms  of  insurance  are  :  GUARANTEE 
COMPANIES  that  act  as  bondsmen,  PLATE  GLASS  INSURANCE,  HAILSTORM 
AND  CYCLONE  INSURANCE,  STEAM  BOILER  INSURANCE,  LIVE  STOCK  IN- 
SURANCE, etc.,  etc. 

671.  Fire  Insurance  is  indemnity  against  loss  or  damage 
by  fire. 

672.  Marine  Insurance  is  indemnity  against  loss  or  dam- 
age to  vessels  and  their  cargoes. 

673.  Accident  Insurance  is  indemnity  against  loss  by 
accidents. 

674.  Health  Insurance  is  a  remuneration  paid  for  loss  of 
lime  or  for  expense  caused  by  ill  health. 

675.  The  Insurer  is  the  party  guaranteeing  against  loss. 

676.  The  Insured  is  the  party  indemnified. 

677.  The  Policy  is  the  contract  of  insurance. 

678.  The  Face  of  the  Policy  is  the  amount  of  insurance 
guaranteed. 

679.  The  Premium  is  the  sum  paid  for  insurance. 

680.  The  Term  of  Insurance  is  the  time  for  which  the 
insurance  is  given. 

681.  There  are  two  principal  kinds  of  insurance  companies  : 
Mutual  and  Non-Mutual. 

682.  Mutual  Companies  are  those  in  which  the  insured 
share  in  the  gains  or  losses. 

683.  The  Non- Mutual  Companies  are  those  owned  ex- 
clusively by  stockholders  and  the  insured  do  not  share  in  the 
gains  or  losses. 

NOTE — Many  companies  combine  the  mutual  and  non-mutual  plans  as 
above  described. 


INSURANCE  189 

Fire  Insurance 

684.  Since  the  premiums  paid  for  fire  insurance  are  esti- 
mated at  a  certain  rate  per  cent.,   the  principles  of  Percentage 
will  apply. 

685.  To  find  the  Premium,  Rate  of  Premium,  and  Face  of 
Policy. 

FORMULA  :  Face  of  Policy  X  Rate  =  Premium. 
Premium  -f-  Rate  =  Face  of  Policy. 
Premium  -H  Face  of  Policy  =  Rate. 

EXAMPLE  :  A  house  valued  at  $4500  is  insured  for  3  years  at 
y±  its  value.  If  the  annual  rate  charged  is  Y\°/o,  what  is  the 
premium  ? 

y*  of  $4500         =  $3000,  face  of  policy. 
$3000  X  3A%  ==  $22.50,  prem.  for  1  year. 
$22.50  X  2         =  $45,  prem.  for  3  years. 

NOTE — Policies  are  issued  for  1  year  or  for  3  years.  The  cost  for  3 
years  is  double  that  for  1  year. 


PRACTICAL  PROBLEMS 
686.     Solve  the  following  : 

1.  How  much  will  it  cost  to  insure  a  house  for  $2500,   the 
rate  of  premium  being  %%  ? 

2.  My  house  is  insured  for  $2200,  and  my  furniture  for  $800. 
What  is  my  premium  at  1J4%  ? 

3.  Brown  insured  his  house  worth  $6000  for  Y\   its  value  in 
the  Northwest  National  for  three  years  at  an  annual  rate  of  70 
cents  on  the  $100.     What  premium  did  he  pay  ? 

4.  The  ^Etna  Insurance  Company  takes  a  year's  risk  of  $8000 
at  a  90  cent  rate.     A  fire  occurs  causing  25%   damage.     What 
is  the  company's  loss? 

5.  A  paid  $29.25  for  insurance  on  his  stock  of  merchandise 
at  a  65  cent  rate.     What  was  the  face  of  his  policy  ? 


190  MODERN    BUSINESS    ARITHMETIC 

6.  If  a  three  years'  policy  at  an  annual  rate  of  70  cents  cost 
$24.50,  what  is  the  amount  of  insurance? 

7.  As  an  agent  my  commission  of  25%   on  insurance  prem- 
iums amounted   to  $2227.86.     What  was  the  total  amount  cov- 
ered, if  the  average  annual  rate  was  60  cents  on  the  $100? 

8.  I  insured  my  dwelling  in  the  Phoenix  Company  for  $3220 
at  1  %  ;  my  household  goods  and  furniture  in  the  Island   Com- 
pany for  $1200,  at  90  cents  ;  my  store  building  for  $1800  in  the 
Lion  Company,   at  l/^%,    and  my   stock    of    merchandise    for 
$12000  in  the  Home  Company,   at  $1.20.     What  was  the  total 
amount  of  premium  paid,  and  what  was  the  average  rate? 

9.  B's  property  valued  at  $14560,  is  insured  for   Y±   its  value 
at  1%%  premium.     A  fire  occurs  causing  a  loss  equal  to  ^  the 
face  of  the  policy.     What  is  B's  loss  if  the  insurance  company 
pay  only  90  cents  on  the  dollar  ? 

10.  The  Hartford  Insurance  Company  took  a  risk  on  a  ware- 
house for  3  years  at  l/^%  premium  and  reinsured  Y\  of  their 
policy  in  the  Commercial  at  1%%.  A  fire  occurred  in  which 
the  entire  plant  was  destroyed.  If  the  loss  of  the  Hartford  Com- 
pany was  $2440,  what  was  the  face  of  the  policy? 


I/ife  Insurance 

687.  Jyife  Insurance  is  a  contract  by  which  the  insurer 
agrees  to  pay  a  beneficiary  a  certain  sum  upon  the  death  of  the 
insured  or  at  a  specified  time. 

688..  The  Beneficiary  is  the  one  named  in  the  policy  to 
receive  the  benefit. 

689.  There  are  many  kinds  of  policies  written  by  life  insur- 
ance companies  ;   among  them  are  :      Ordinary  Life  Policy,  Lim- 
ited Life  Policy,  Endowment  Policy,  Annuity  Policy,  Midual Poli- 
cies, etc. 

690.  The  Ordinary  Life  Policy  requires  regular  prem- 
iums to  be  paid  during  life,  and  the  benefit  to  be  paid  only  upon 
the  death  of  the  insured. 


INSURANCE 


191 


691.  The  Limited  Life  Policy  requires  premiums  to  be 
paid  for  a  stated  number  of  years,  the  benefit  to  be  paid  upon 
the  death  of  the  insured. 

TABLE  OF  INSURANCE  RATES,  1908 

Premium  Rates  for  $1000  of  Insurance 


> 
c 

R 

ORDINARY  LIFE 

20-YR.  ENDOWMENT 

20-PAYMENT  LIFE 

Annual 

Semi- 
Annual 

Quar- 
terly 

Annual 

Semi- 
Annual 

Quar- 
terly 

Annua' 

Semi- 
Ann  ual 

Quar- 
terly 

20 

$15.50 

$8.06 

$1.11 

$42.79 

$22.25 

$11.34 

$23.31 

$12.13 

$6.18 

21 

15.84 

8.24 

4.20 

42.83 

22.28 

11.35 

23.69 

12.32 

6.28 

22 

16.19 

8.42 

4.29 

42.89 

22.31 

11.37 

24.08 

12.53 

6.39 

23 

16.57 

8.62 

4.40 

42.94 

22.33 

11.38 

24.48 

12.73 

6.49 

24 

16.96 

8.82 

4.50 

43.00 

22.36 

11.40 

24.91 

12.96 

6.61 

—25— 

17.37 

9.04 

4.61 

43.05 

22.39 

11.41 

25.35 

13.19 

6.72 

26 

17.80 

9.26 

4.72 

43.12 

22.43 

11.43 

25.80 

13.42 

6.84 

27 

18.26 

9.50 

'   4.84 

43.20 

22.47 

11.45 

26.27 

13.66 

6.97 

28 

18.73 

9.74 

4.97 

43.27 

22.50 

11.47 

26.76 

13.92 

7.10 

29 

19.24 

10.01 

5.10 

43.36 

22.55 

11.49 

27.27 

14.18 

7.23 

—30— 

19.77 

10.28 

5.39 

43.46 

22.60 

11.52 

27.80 

14.46 

7.37 

31 

20.33 

10.58 

5.24 

43.57 

22.66 

11.55 

58.36 

14.75 

7.52 

32 

20.92 

10.88 

5.55 

43.69 

22.72 

11.58 

28.94 

15.05 

7.67 

33 

21.54 

11.20 

5.71 

43.81 

22.79 

11.61 

29.53' 

15.36 

7.83 

34 

22.20 

11.55 

5.89 

43.97 

22.87 

11.66 

30.16 

15.69 

8  DO 

—35— 

22.90 

11.91 

6.07 

44.13 

22.95 

11.70 

30.83 

16.04 

8.17 

36 

23.63 

12.29 

6.27 

44.31 

23.05 

11.75 

31.51 

16.39 

8.35 

37 

24.40 

12.69 

6.47 

44.52 

23.15 

11.80 

62.22~ 

16.76 

8.54 

'  38 

25.23 

13.12 

6.69 

44.75 

23  27 

11.86 

32.97 

17.15 

8.74 

39 

26.11 

13.58 

6.92 

45.00 

23.40 

11.93 

33.76 

17.56 

8.95 

—  40  — 

27.03 

14.06 

7.17 

45.30 

23.56 

12.01 

34.59 

17.99 

9.17 

41 

28.01 

14.57 

7.43 

45.62 

23.73 

12.09 

35.46 

18.44 

9.40 

42 

29.05 

15.11 

7.70 

45.99 

23.92 

12.19 

36.38 

18.92 

9.64 

43 

30.16 

15.69 

8.00 

46.40 

24.13 

12.30 

37.35 

19.43 

9.90 

44 

31.35 

16.31 

8.31 

46.87 

24.38 

12.42 

38.37 

19.96 

10.17 

—  45— 

32.60 

16.96 

8.64 

47.39 

24.65 

12.56 

39.45 

20.52 

12.17 

46 

33.94 

17.65 

9.00 

47.97 

24.95 

12.72 

40.59 

21.11 

10.46 

47 

35.36 

18.39 

9.37 

48.63 

25.29 

12.89 

41.81 

21.75 

10.76 

48 

36.88 

19.18 

9.78 

49.37 

25.68 

13.09 

43.10 

22  42 

11.08 

49 

38.50 

20.02 

10.21 

50.19 

26.10 

13.30 

44.47 

23!l3 

11.43 

—50— 

40.24 

20.93 

10.67 

51.11 

26.58 

13.55 

45.92 

23.88 

11.79 

51 

42.08 

21.89 

11.16 

52.13 

27.11 

13.82 

47.48 

24.69 

12.59 

52 

44.03 

22.90 

11.67 

53.25 

27.69 

14.12 

49.13 

25.55 

13.02 

53 

46.13 

23.99 

12.23 

54.51 

28.35 

14.45 

50.88 

26.46 

13.49 

54 

48.37 

25.16 

12.82 

55.89 

29.07 

14.81 

52.77 

27.44 

13.99 

—55— 

50.75 

26.39 

13.45 

57.43 

29.87 

15.22 

54.79 

28.49 

14.52 

56 

53.29 

27.71 

14.13 

59.13 

30.75 

15.67 

56.96 

29.62 

15.10 

57 

56.02 

29.13 

14.85 

61.00 

31.72 

16.17 

59.28 

30.83 

15.71 

58 

58.91 

30.64 

15.62 

63.05 

32.79 

16.71 

61.76 

32.12 

16.37 

59 

62.03 

32.26 

16.44 

65.32 

33.97 

17.31 

64.44 

33.51 

17.08 

—60— 

65.41 

34.02 

17.34 

67.82 

35.27 

17.98 

67.33 

35.02 

17.85 

692.  The  Endowment  Policy  requires  premiums  to  be 
paid  for  a  stated  number  of  years  or  until  the  death  of  the  in- 
sured, the  benefit  to  be  paid  at  the  end  of  the  stated  time  or 
upon  the  death  of  the  insured. 


192  MODERN    BUSINESS    ARITHMETIC 

693.  Mutual  Policies  are  those  issued  by  mutual  insur- 
ance companies  which  permit  the  insured  to  participate  in  the 
profits  of  the  business,  thereby  reducing  the  rate  of  premium. 

694.  The  Surrender  Value  is  the  amount  that  the  com- 
pany will  pay  upon  surrender  of  the  policy. 

695.  To   find    the  Annual  Premium  on  $1000   consult  the 
preceeding  table. 

EXAMPLE  :     A  man  29  years  of  age  takes  out  a  20  annual  pay- 
ment policy  for  $5000.     What  annual  premium  does  he  pay? 

29  yrs.  and  20  annual  payments  =  $27.27  premium. 
$27.27  X  5  =  $136.35,  annual  premium  on  $5000. 


PRACTICAL  PROBLEMS 
696.     Solve  the  following  : 

1.  What  will  be  the  annual  premium  on  an  ordinary  life  pol- 
icy for  $2000  at  the  age  of  42  years  ? 

2.  A  man  takes  out  a  20  year  endowment  policy  at  the  age 
of  30  years  for  $4000.     What  annual  rate  will  he  pay  ? 

3.  What  will  a  limited  20  payment  life  policy  for  $6000  cost 
me  annually  if  taken  at  the  age  of  25  years  ? 

4.  A,  at  the  age  of  32  years,  had  his  life  insured  for  $1000 
under  the  ordinary  life  plan.     If  he  had  died  at  the  age  of  54 
years,  how  much  more  would  his  heirs  receive  than  had  been 
paid  in? 

5.  Wishing  to  take  out  insurance  at  the  age  of  27  years,   I 
decided  to  adopt  the  20  year  endowment  plan.     If  the*  face  of 
the  policy  was  $2500,  what  would  the  total  insurance  cost  me  ? 

6.  What  will  be  the  excess  received  over  that  paid  to  the 
heirs  of  one  who  at  the  .age  of  40  takes  out  a  limited  20  pay- 
ment life  policy  for  $10000,  and  dies  at  the  age  of  70  ? 

7.  What  is  the  difference  in  cost  of  a  20  year  endowment 
policy  for  $3000  at  the  age  of  37  years,  and  a  20  payment  policy 
for  the  same  amount,  at  the  same  a^c  ? 


INSURANCE 


193 


8.  The  Metropolitan  Life  Insurance  Company  issues  an  ordi- 
nary life  policy  for  John  Jones,  aged  22  years,  for  $5000.     If  the 
heirs  received  $4433.35  more  than  had  been  paid   in,   how  old 
was  the  insured  at  the  time  of  his  death  ? 

9.  The  New  York  Life  Insurance  Company  issued  a  20  year 
endowment  policy  to  a  man  aged  45  years.     If  he  dies  at  the  age 
of  57  years  and  his  heirs  receive  $1431.32  more  than  has  been 
paid  to  the  company,  what  was  the  face  of  the  policy? 

10.  The  Equitable  Life  Insurance  Company  issues  a  20  pay- 
ment life  policy  for  $25000  to  a  person  who  lived  long  enough  to 
pay  15  annual  premiums  amounting  to  $17220.  What  was  the 
age  of  the  insured  at  the  time  of  his  death  ? 


Outline  for  Review 


V.  Stocks  and  Bonds : 

1.  Corporation. 

2.  Articles  of  Incorporation. 

3.  Capital  Stock. 

4.  Stocks,  Certificates. 

5.  Par  Value,  Market  Value. 

6.  Premium,  Discount. 

7.  Installment,    Assessment, 

Dividend. 

8.  Bonds,  Registered  Bonds, 

Coupon  Bonds. 

9.  Treasury  Stock,  Preferred 

Stock,  Watered  Stock. 
10.  Cases. 

VI.  Taxes  : 

1.  Definitions. 

2.  Property  Tax,  Poll  Tax. 

3.  Real  Estate,  Personal  Prop- 

erty. 

4.  Assessor,  Tax  Colector. 

5.  Collection. 

6.  Assessment  Roll. 


VIL     U.  $.  Customs  or 
Duties : 

1.  Definitions. 

2.  Custom  House,  Port  of 

Entry. 

3.  Manifest,  Clearance. 

4.  Ad  valorem  Duty,  Specific 

Duty. 

5.  Tare,  Leakage,  Breakage. 

6.  Gross  Weight,  or  Gross 

Value. 

7.  Net  Weight,  or  Net  Value. 

VIII.    Insurance : 

1.  Definitions. 

2.  Fire,  Marine,  Accident, 

Health. 

3.  Insurer,  Insured. 

4.  Policy,  Premium. 

5.  Mutual  and  Non-Mutual 

Companies. 

6.  Life  Insurance. 

7.  Beneficiary. 

8.  Kinds  of  Policies. 

9.  Surrender  Value. 


INTEREST 


697.  Interest  is  the  sum  paid  for  the  use  of  money  or  other 
value. 

698.  There  are  three  methods  of  computing  interest : 

1.  By  Simple  Interest. 

2.  By  Periodic  Interest. 

3.  By  Compound  Interest. 

699.  All  of  these  methods  require  the  element  of  time  in  ad- 
dition to  the  regular  elements  of  Percentage. 

700.  The  Principal  is  the  money  or  value  for  which  inter- 
est is  paid. 

701.  The  Rate  of  Interest  is  the  amount  paid  for  the  use 
of  $1  for  1  year. 

702.  The  Time  is  the  period  for  which  the  interest  is  com- 
puted. 

703.  The  Amount  is  the  sum  of  the  principal  and  interest. 

704.  Legal  Interest  is  the  rate  of  interest  established  by 
law. 

705.  Usury  is  a  higher  rate  than  the  law  allows. 

706.  Since  interest  is  computed  at  a  certain  rate  percent., 
the  cases  of  Percentage  apply,  and  the  additional  element  of  time 
is  added. 

707.  The  elements  are  as  follows  : 

1.  The  Principal  =  Base. 

2.  The  Interest  =  Percentage. 

3.  The  Rate  of  Interest  =  Rate. 

4.  The  Amount  =  Principal  +  Interest. 

5.  The  Time. 

In  computing  Common  Interest,  360  days  are  considered  a 
year,  and  30  days  a  month.  In  computing  Exact  Interest,  365 
days  are  considered  a  year. 


Simple  Interest 


708.     Simple  Interest  is  interest  on  the  principal  only  for 
the  given  time  and  rate. 


CASE  I 

709.  Given,  the  Principal,  Time,  and  Rate  to  find  the 

Interest. 

710.  Three  Methods  of  finding  simple  interest  are  given 
in  this  work.     1.  Cancellation  Method.     2.  Six  Per  Cent.  Meth- 
od.    3.  Bankers'  Method. 

For  Cancellation  Method  turn  to  page  55  of  this  book. 


Six  Per  Cent.  Method 

711.  In  the  Six  Per  Cent.  Method,  12  months  of  30  days 
each,  or  360  days  constitute  a  year.  The  analysis  of  the  method 
is  as  follows  : 

FOR  YEARS : 

The  interest  on  $1  for  1  year  or   12   months   at  6%  =  $.06. 
Therefore,  ~to  find  the  interest  on  $1  for  years,   multiply  $.06  by 
the  number  of  years. 

FOR  MONTHS  : 

The  interest  on  $1  for  2  months  =  \  of  $.06  or  $.01. 
Therefore,  to  find  the  interest  in  cents  on  $1  for  months,   divide 
the  number  of  months  by  2. 

FOR  DAYS  : 

The  interest  on  $1  for  1  month  or  30  days  =  \  of  $.01  or  $.005. 
The  interest  on  $1  for  6  days  =  £  of  $.005  or  $.001. 

Therefore,  to  find  the  interest  in  mills  on  $1  for  days,  divide  the 
number  of  days  by  6 . 

SUMMARY  I 

$.06  X  No.  of  years  =  Int.  on  $1  expressed  in  cents. 
No.  of  months  -5-  2  =  Int.  on  $1  expressed  in  cents. 
No.  of  days  -5-  6  =  Int.  on  $1  expressed  in  mills. 


196  MODERN    BUSINESS    ARITHMETIC 

EXAMPLE  :     Find  the  interest  on  $200  for  4   years   8  months 
12  days  at  6%. 

$.06  X  4,  number  of  years  =  $.24    int.  on  $1  for  4  years. 
8  months  -^-2  =     .04    int.  on  $1  for  8  months. 

12  days  -*-  6  =     .002  int.  on  $1  for  12  days. 

$.282  int.  on  $1  for  whole  time. 
$.282  X  $200  =  $56.40  total  interest. 

712.     If  the  rate  per  cent,  is  other  than  6%  take  J  of  the  in- 
terest at  6%  and  multiply  by  the  rate  required. 


PRACTICAL  PROBLEMS 

713.     Solve  the  following  by  6%  method  : 

1.  Find  the  interest  on  $1  for  2  yrs.  10  mo.  15  ds.  at  6%. 

2.  Find  the  interest  on  $400  for  1  yr.  6  mo.  24  ds.  at  6%. 

3.  Find  the  interest  on  $750  for  5  yrs.  4  mo.  27  ds.  at  6%. 

4.  Find  the  interest  on  $960  for  3  yrs.  3  mo.  3  ds.  at  6%. 

5.  Find  the  interest  on  $1500  for  4  yrs.  11  mo.  23  ds.  at  6%. 

6.  Find  the  interest  on  $3000  for  3  yrs.  8  mo.  21  ds.   at  7%. 

7.  Find  the  interest  on  $5000  for  7  yrs.  7  mo.  7  ds.  at  7%. 

8.  Find  the  amount  of  $720  on  interest  for  2  yrs.   5  mo.    12 
ds.  at  6%. 

9.  A  note  for  $540  draws  interest  for  9  mo.   18   ds.   at   8%. 
What  is  the  amount  due  ? 

10.  My  note  for  $1000  at  9%  has  been  running  1  yr.  10  mo. 
21  ds.  If  I  have  already  paid  the  interest  for  6  months,  what 
amount  will  now  be  due  ? 


Bankers'  Method 

714.  The  Bankers'  Method  of  computing  interest  is  based 
upon  the  fact  that  by  pointing  off  two  places  (  dividing  by  100  ) 
in  the  principal,  the  result  will  be  the  interest  at  any  rate  for  as 
many  days  as  the  rate  is  contained  in  360,  the  number  of  days  in 
a  year. 


INTEREST  197 

715.  By  pointing  off  two  places  the  interest  on  any  principal 
is  found  : 

At    2%  for  180  days,  the  basis  of  time  at    2%. 

At    3%  for  120  days,  the  basis  of  time  at    3%. 

At    4%  for  90  days,  the  basis  of  time  at    4%. 

At    5%  for  72  days,  the  basis  of  time  at    5%. 

At    6%  for  60  days,  the  basis  of  time  at    6%. 

At    8%  for  45  days,  the  basis  of  time  at    8%. 

At    9%  for  40  days,  the  basis  of  time  at    9%. 

At  10%  for  36  days,  the  basis  of  time  at  10%. 

At  12%  for  30  days,  the  basis  of  time  at  12%. 

At  15%  for  24  days,  the  basis  of  time  at  15%. 

At  18%  for  20  days,  the  basis  of  time  at  18%. 

At  20%  for  18  days,  the  basis  of  time  at  20%. 

At  24%  for  15  days,  the  basis  of  time  at  24%. 

716.  To  find  the  interest  at  7%,  increase  the  interest  at  6% 
by  I  of  itself.     To  find  the  interest  at  11%,  increase  the  interest 
at  10%  by  A  of  itself. 

717.  To  find  the  interest  for  any  number  of  days,    increase 
or  decrease  the  interest  for  the  basis  of  time  by  using    aliquot 
parts. 

718.  The  Bankers'  Method  is  particularly  adapted  to  short 
periods  of  time,  and  is  not  recommended  except  when  the  time 
is  expressed  in  days. 

EXAMPLE  :     Find  the  interest  on  $450  for  36  days  at  6%. 

Pointing  off  two  places  =  $4.50  interest  for  60  days  at  6%. 
\  of  $4.50  =  $2.25  interest  for  30  days, 
i  of  $2.25  =       .45  interest  for  6  days. 
$2.70  interest  for  36  days. 

EXAMPLE  :     Find  the  interest  on  $960  for  108  days  at  8% . 

Pointing  off  two  places  =  $9.60  interest  for  45  days  at  8%. 
Multiplying  $9.60  by  2  =  $19.20  interest  for  90  days. 
\  of  $9.60  =      3.20  interest  for  15  days, 
i  of  $3.20  =         .64  interest  for  3  days. 

$23.04  interest  for  108  days. 

NOTE-  -Notice  that  Aliquot  parts  are  prominent  in  much  of  the  above 
work. 


198  MODERN    BUSINESS    ARITHMETIC 

719.     Solve  the  following  by  Bankers'  Method  ; 

1.  Find  the  interest  on  $342  for  33  days  at  6%. 

2.  Find  the  interest  on  $175  for  27  days  at  6%. 

3.  Find  the  interest  on  $924  for  54  days  at  8%. 

4.  Find  the  interest  on  $3000  for  78  days  at  5%. 

5.  Find  the  interest  on  $2150  for  126  days  at  9%. 

6.  Find  the  interest  on  $215.60  for  88  days  at  10% 

7.  Find  the  interest  on  $321.75  for  37  days  at  12% 

8.  Find  the  interest  on  $810  for  76  days  at  7%. 

9.  Find  the  interest  on  $1350  for  111  days  at  11%. 
10.  Find  the  interest  on  $427.20  for  48  days  at 


CASE  II 

720.     Given,  the  Interest,  Rate,  and   Time  to  find  the 
Principal. 

Use  the  cancellation  method  as  indicated  below .     The  Interest  will, 
be  the  dividend  and  the  Time  multiplied  by  the  Rate  the  divisor. 

FORMULA  :     Interest  -H  Rate  X  Time  expressed  in  years  = 
Principal. 

EXAMPLE  :     The  interest  is  $2.80,  the  time  35  days,   and  the 
rate  6%.     What  is  the  principal ? 


60 


300  ds. 


Int.,8 


($     ),  principal 
3$  ds.,  time 
.00,        rate 


60  X  $8  =  $480  ==  Principal. 
721.     Solve  the  following  by  cancellation  method  : 

1.  What  principal  will  produce  an  interest  of  $300  in  48  ds., 
at6%? 

2.  An  interest  of  $8.26  in  59  ds.  at  7%  ? 

3.  An  interest  of  $29.10  in  97  ds.  at  9%  ? 

4.  An  interest  of  $8.55  in  114  ds.  at  5%  ? 

5.  An  interest  of  $4.62  in  3  mo.  9  ds.  at  6%  ? 


INTEREST  199 

6.  An  interest  of  $58  in  1  yr.  2  mo.  15  ds.  at  8%  ? 

7.  An  interest  of  $214.20  in  2  yrs.  6  mo.  18  ds.  at  7%  ? 

8.  An  interest  of  $43. 08^  in  1  yr.  5  mo.  7  ds.  at  6%  ? 

9.  An  interest  of  $84.50  in  39  ds.  at  4%  ? 

10.     An  interest  of  $2133.60  in  320  ds.  at  10%  ? 


CASE  III 

722.  Given  the  Interest,  Principal,  and  Time  to  find 
the  Rate. 

Use  the  cancellation  method  as  indicated  below.  The  Interest 
will  be  the  dividend,  and  the  Principal  multiplied  by  the  Time  the 
divisor. 

FORMULA  :     Int.  -+-  Prin.  X  Time  expressed  in  yrs.  =  Rate. 

EXAMPLE  :     At  what  rate  will  $450  gain  $26.25  in  10  mo.  ? 

* 


7%,  Ans. 
723.     Solve  the  following  : 

1.  At  what  rate  per  cent,  will  $540  gain  $3.15  in  35  ds.  ? 

2.  Will  $1170  gain  $54.60  in  7  mo.  ? 

3.  Will  $510  gain  $61.20  in  1  yr.  6  mo.  ? 

4.  Will  $825  gain  $9.90  in  1  mo.  24  ds.  ? 

5.  Will  $1260  gain  $52.92  in  7  mo.  6  days? 

6.  Will  $47.50  gain  $4.94  in  1  yr.  3  mo.  18  ds.  ? 

7.  Will  $325.50  gain  $24.52  in  11  mo.  9  ds.  ? 

8.  Will  $1350  gain  $36.45  in  216  ds.  ? 

9.  Will  $2500  gain  $475  in  171  ds.  ? 

10.     Will  $8000  gain  $810  in  1  yr.  4  mo.  6  ds.  ? 


CASE  IV 

724.  Given,  the  Interest,  Principal,  and  Rate  to  find 
the  Titne. 

Use  the  cancellation  method  as  indicated  in  the  following  solution. 
The  Interest  will  be  the  dividend  and  the  Principal  multiplied  by 
the  Rate  the  divisor. 


200  MODERN    BUSINESS    ARITHMETIC 

FORMULA  :     Int.  -*-  Prin.  X  Rate  =  Time. 

EXAMPLE:     In  what  time  will  $720  produce  $7.92  interest  at 
*<&  ? 


$00  ds. 


66 


int., 


Also : 


(        ) 


mo. 

2.2 


.00  $102 


(       ) 

.00 


66  ds.,  Ans.  2.2  mo.,  or  2  mo.  6  ds.,  Ans. 

725.     Solve  the  following  : 

1.  In  what  time  wall  $320  earn  $12.80  interest  at  6%  ? 

2.  Will  $480  earn  $6.16  interest  at  6%  ? 

3.  Will  $580  earn  $5.80  interest  at  8%  ? 

4.  Will  $780  earn  $32.76  interest  at  7%  ? 

5.  Will  $960  earn  $18.80  interest  at  5%  ? 

6.  Will  $1200  earn  $139.50  interest  at  9%  ? 

7.  Will  $1400  earn  $119.70  interest  at  6%  ? 

8.  Will  $2100  earn  $338.10  interest  at  7%  ? 

9.  Will  $4500  earn  $175.50  interest  at  4^  %  ? 
10.  Will  $18680  earn  $700.50  interest  at  1%  %  ? 


CASE  V 

726.  Given,   the  Amount,  Rate,  and   Time  to  find  the 
Principal. 

Divide  the  given  Amount  by  the  amount cf  $1  for  the  given  Time 
and  Rate. 

FORMULA  :     Amt.  -5-  $1  -f-  (Rate  X  Time)  ==  Prin. 
EXAMPLE  :     What  principal  will  amount  to  $430.50  in  5  mo. 
at  6%  ? 

$1.00  X  .06  X  5/i2  yr.  =  .02^,  Int.  on  $1  for  5  mo. 

$1.00  +  .02^  =  $1.025,  Amt.  of  $1  for  5  mo. 

$430.50  -*-  $1.025  =  $420,  Prin.,  Ans. 

727.  Solve  the  following  : 

1.  What  principal  will  amount  to  $250.80  in  9  mo.  at  6%  ? 

2.  Will  amount  to  $333.25  in  1  yr.  3  mo.  at  6%  ? 

3.  Will  amount  to  $520.53  in  2  yr.  5  mo.  at  8%  ? 

4.  Will  amount  to  $675.08  in  33  ds.  at  5%  ? 


INTEREST  201 

5.  Will  amount  to  4113.90  in  71  ds.  at  8%  ? 

6.  Will  amount  to  $1313.27  in  3  mo.  22  ds.  at  9%  ? 

7.  Will  amount  to  $2374.50  in  1  yr.  4  mo.  18  ds.  at  4%  ? 

8.  Will  amount  to  $5262.60  in  2  yr.  1  mo.  21  ds.  at  4l/2%  ? 

9.  Will  amount  to  $7656.25  in  75  ds.  at  10%  ? 

10.  Will  amount  to  12977.50  in  1  yr.  1  mo.  1  da.  at 


Exact  Interest 

728.  Exact  Interest  is  the  interest  on  any  sum  when  the 
time  is  computed  on  the  basis  of  365  days  to  the  year,  or  the  ex- 
act year.     In  leap  years  366  days  is  the  basis  of  exact  interest. 

729.  The  interest  for  whole  years  is  the  same  as  in  common 
interest,  therefore  the  exact  method  applies  only  when  the  time 
is  less  than  a  year  expressed  in  days. 

730.  In  ordinary  business  transactions  this  method  is  seldom 
used  but  is  strictly  legal. 

731.  The  cancellation  method  of  computing   exact  interest  is 
recommended,  but  it  can  also  be  found  by  deducting  -^  from  the 
common  interest,  as  the  5  days  difference  in  the  exact  and  com- 
mon years  is  3! 3  or  7*5. 

EXAMPLE  :     Find  the  exact  interest  on  $540  for  146   days  at 
6%. 


108 

146 


ilo.  14  Common  Int. 


Or, 

1402 

.06 


.18  Ext.  Int.,  $12.96,  Ans. 


$12.96  Exact  Int. 
732.     Solve  the  following  : 

1.  Find  the  exact  interest  of  $730  for  33  ds.  at  6%. 

2.  Of  $1095  for  42  ds.  at  7%. 

3.  Of  $292  for  45  ds.  at  &% . 

4.  Of  $80.30  for  77  ds.  at  5%. 

5.  Of  $500  for  90  ds.  at  6%. 

6.  Of  $1200  for  110  ds.  at  9%. 

7.  Of  $1800  for  132  ds.  at  4%. 


202  MODERN  BUSINESS  ARITHMETIC 


8.  Of  $3000  for  219  ds.  at 

9.  Of  $4380  for  134  ds.  at  10%. 

10.     Of  $549  for  256  days  of  a  leap  year  at 


Annual,  Semi- Annual,  and  Quarterly  Interest 

733.  Annual  Interest  is  the  simple  yearly  interest  on  the 
principal,  and  the  simple  interest  on  such  interest  remaining  un- 
paid. 

734.  Semi- Annual  Interest  is  the  simple  half-yearly  in- 
terest on  the  principal,  and  the  simple  interest  on  such  interest 
remaining  unpaid. 

735.  Quarterly  Interest  is  the  simple  quarterly  interest 
on  the  principal,  and  the  simple  interest  011  such  interest  remain- 
ing unpaid. 

736.  Given,  the  Principal,  Rate,  and  Time  to  find  the 
Annual,  Semi-Annual,  and  Quarterly  Interest. 

1.  Find  the  interest  on  the  principal  for  the  whole  time. 

2.  Find  the  interest  on  the  interest  for*  the  year,   half  year,   or 
quarter  for  the  total  time  that  the  interest  payments  are  delinquent. 

3.  The  interest  due  will  be  the  sum  of  the  interest  on,   the  prin- 
cipal and  the  interest  on  the  unpaid  interest. 

EXAMPLE  :  Find  the  amount  due  on  a  note  for  $1200  dated 
July  10,  1904  and  paid  October  25,  1907,  at  6%,  interest  to  be 
paid  annually. 

Yr.       Mo.    Da. 

October  25,  1907  =  1907     10     25 

July  10,  1905         =  1904       7     10 

Dif.  in  time  =          3       3     15 

a.  Simple  int.  on  $1200  for  3  yr.  3  mo.  15  ds.  at  6%  a=  $237. 

b.  Simple  annual  int.  on  $1200  at  6%  ==  $72. 

Int.  on  $72  due  end  of  1st  yr.  runs     2  yr.     3  mo.   15  ds. 
Int.  on  $72  due  end  of  2d  yr.  runs     1  yr.     3  mo.   15  ds. 

Int.  on  $72  due  end  of  3d  yr.  runs       3  mo.   15  ds. 

Total  int.  on  $72  runs    3  yr.   10  mo.   15  ds. 

c.  Int.  on  $72  for  3  yr.  10  mo.  15  ds.  =  $16.74. 

d.  Int.  on  Prin.  $237  +  $16.74  =  $253.74  total  annual  int. 

e.  Prin.,  $1200  +  Int.,  $253.74  =  Amt.  due,  $1453.74,  Ans. 


INTEREST  203 

737.     Solve  the  following  : 

1.  Find    the    total   interest,   payable  annually,    on  $900   for 
4  yrs.  6  mo.  at  6% . 

2.  Annually,  on  $1500  for  5  yrs.  4  mo.  at  6%. 

3.  Annually,  on  $1800  for  3  yrs.  7  mo.  12  ds.  at  6%. 

4.  Annually,  on  $2400  for  5  yrs.  9  mo.  27  ds.  at  8%. 

5.  Semi-annually,  on  $600  for  2  yrs.  at  8%. 

6.  Semi-annually,  on  $1050  for  1  yr.  9  mo.  at  8%. 

7.  Semi-annually,  on  $4500  for  3  yrs.  2  mo.  10  ds.  at  6%. 

8.  Quarterly,  on  $300  for  1  yr.  5  mo.  at  8%. 

9.  Quarterly,  on  $2000  for  2  yrs.  1  mo.  15  ds.  at  10%. 
10.     Quarterly,  on  $4200  for  3  yrs.  3  mo.  3  ds.  at  7%. 


Questions  for  Review 

1.  Define  Interest.     Principal.     Rate.     Time.     Amount. 

2.  What  three  methods  are  used  in  computing  Interest? 

3.  What  i^ Legal  Interest?     Usury? 

4.  What  is  Simple  Interest? 

5.  Explain  the  Six  Per  Cent.  Method  of  finding  interest. 

6.  Explain  the  Bankers'  Method  of  finding  interest? 

7.  Write  the  formulae  for  finding  the  different  elements  in 
the  problems  of  Interest. 

8.  What  is  Exact  Interest?     How  much  less  is  it  than  Com- 
mon Interest  ?     Why  ? 

9.  What  is  meant  by  Annual,   Semi- Annual,  and  Quarterly 
Interest  ? 

10.     Describe  the  correct  method  of  finding  Annual,   Semi- An- 
nual, and  Quarterly  Interest? 


Compound  Interest 

738.  Compound  Interest  is  the  interest  on  the  principal 
and  also  upon  the  unpaid  interest  when  due. 

739.  In  computing  compound  interest  the  interest  for  a  cer- 
tain period  when  due  is  added  to  the  principal,  and  this  amount 
is  the  new  principal  for  the  next  period. 

740.  The  Period  of  computation  may  be  yearly,   semi-an- 
nually,  or  quarterly  as  agreed  upon.     Compound  interest  is  not 
lawful  except  upon  specific  contract. 

741.  Given,  the  Principal,  Rate,  and   Time  to  find  the 
Compound  Interest. 

Find  the  amount  of  the  principal  for  the  first  period ;  this 
amount  will  be  the  principal  for  the  second  period ;  continue  in  like 
manner  for  the  full  tune.  The  final  amount  less  the  first  principal 
will  be  the  compound  interest. 

EXAMPLE  :  Find  the  interest  of  $400  for  3  yr.  4  mo.  24  ds. 
at  6%,  compounded  annually. 

$400.00  =  Principal. 

24.00  =  Int.  on  $400  for  1  yr.  at  6%. 
424.00  =  Amt.  at  close  of  first  year. 

25.44  =  Int.  on  $424  for  2d  year. 
449.44  =  Amt.  at  close  of  2d  year. 

26.97  =  Int.  on  3d  principal. 
476.41  =  Amt.  at  close  of  3d  year. 

11.43  =  Int.  for  4  mo.  24  ds. 
487.84  =  Amt.  at  close  of  time. 
400.00  =  First  principal. 
$87.84  =  Compound  interest,  Ans. 

742.  Solve  the  following  : 

1 .  Find  the  interest  compounded  annually  on  $600  for  2  yrs. 
at  6%. 

2.  Annually  on  $1000  for  4  yrs.  at  6%. 

3.  Annually  on  $1200  for  6  yrs.  at  8%. 

4.  Annually  on  $2100  for  10  yrs.  at  10%. 


INTEREST 


205 


5.  Semi-annually  on  $1500  for  2  yrs.  6  mo.  at  6%. 

6.  Semi-annually  on  $5400  for  4  yrs.  9  mo.  at  7%. 

7.  Semi-annually  on  $7200  for  8  yrs.  8  mo.  15  ds.  at  6%. 

8.  Quarterly  on  $900  for  1  yr.  8  mo.  12  ds.  at  8%. 

9.  Quarterly  on  $1300  for  2  yrs.  2  mo.  3  ds.  at  10%. 
10.  Quarterly  on  $2000  for  5  yrs.  5  mo.  6  ds.  at  6%. 

743.  The    computation    of    compound    interest    is    greatly 
abbreviated  by  using  the  following  table  : 

744.  To  use  the  table,   multiply  the  amount  of  $1   for  the 
number  of  periods  at  the  given  rate,  by  the  given  principal ;  the 
result  will  be  the  amount  of  the  principal  for  the  whole  periods. 
Interest  for  additional  time  is  added  as  usual. 

NOTE — For  semi-annual  interest,  double  the  years  and  take  half  the 
annual  rate.  For  quarterly  interest,  take  four  times  the  years  and  one- 
fourth  the  annual  rate. 

COMPOUND  INTEREST  TABLE 

Showing  the  amount  of  $1  at  compound  interest  at  various  rates  of  in- 
terest for  specified  periods. 


Yr 

2\  perct. 

3  per  ct. 

3J  perct. 

4  per  ct. 

5  per  ct. 

6  per  ct. 

1 

1.025000 

1.030000 

1.035000 

1.040000 

1.050000 

1.060000 

2 

1.050625 

1.060900 

1.071225 

1.081600 

1.102500 

1.123600 

3 

1.076891 

1.092727 

1.108718 

1.124864 

1.157625 

1.191016 

4 

1.103813 

1.125509 

1.147523 

1.169859 

1.215506 

1.262477 

5 

1.131408 

1.159274 

1.187686 

1.216653 

1.276282 

1.338226 

6 

1.159693 

1.194052 

1.229255 

1.265319 

1.340096 

1.418519 

7 

1.188686 

1.229874 

1.272279 

1.315932 

1.407100 

1.503630 

8 

1.218403 

1.266770 

1.316809 

1.368569 

1.477455 

1.593848 

9 

1.248863 

1.304773 

1.362897 

1.423312 

1.551328 

1.689479 

10 

1.280085 

1.343916 

1.410599 

1.480244 

1.628895 

1.790848 

11 

1.312087 

1.384234 

1.459970 

1.539454 

1.710339 

1.898299 

12 

1.344889 

1.425761 

1.511069 

1.601032 

1.795856 

2.012197 

13 

1.378511 

1.469534 

1.563956 

1.665074 

1.885649 

2.132928 

14 

1.412974 

1.512590 

1.618695 

1.731676 

1.979932 

2.260904 

15 

1.448298 

1.557967 

1.675349 

1.800944 

2.078928 

2.396558 

16 

1.484506 

1.604706 

1.733986 

1.872981 

2.182875 

2.540352 

17 

1.521618 

1.652848 

1.794676 

1.947901 

2.292018 

2.692773 

18 

1.559659 

1.702433 

1.857489 

2.025817 

2.406619 

2.854339 

19 

1.598650 

1.753506 

1.922501 

2.106849 

2.526950 

3.025600 

20 

1.638616 

1.806111 

1.989789 

2.191123 

2.653298 

3.207136 

206 


MODERN  BUSINESS  ARITHMETIC 


Yr 

7  per  ct. 

8  per  ct. 

9  per  ct. 

lOperct. 

11  per  ct. 

12  per  ct. 

1 

1.070000 

1.080000 

1.090000 

1.100000 

1.110000 

1.120000 

2 

1.144900 

1.166400 

1.188100 

1.210000 

1.232100 

1.254400 

3 

1.225043 

1.259712 

1.295029 

1.331000 

1.367631 

1.404908 

4 

1.310796 

1.360489 

1.411582 

1.464100 

1.518070 

1.573519 

5 

1.402552 

1.469328 

1.538624 

1.610510 

1.585058 

1.762342 

6 

1.500730 

1.586874 

1.677100 

1.771561 

1.870414 

1.973822 

7 

1.605781 

1.713824 

1.828039 

1.948717 

2.076160 

2.210681 

8 

1.718186 

1.850930 

1.992563 

2.143589 

2.304537 

2.475963 

9 

1.838459 

1.999005 

2.171893 

2.357948 

2.558036 

2.773028 

10 

1.967151 

2.158925 

2.367364 

2.593742 

2.839420 

3.105848 

11 

2.104852 

2.331639 

2.580426 

2.853117 

3.151757 

3.478549 

12 

2.252192 

2.518170 

2.812665 

3.138428 

3.498450 

3.895975 

13 

2.409845 

2.719624 

3.065805 

3.452271 

3.883279 

4.363492 

14 

2.578534 

2.937194 

3.341727 

3.797498 

4.310440 

4.887111 

15 

2.759031 

3.172169 

3.642482 

4.177248 

4.784588 

5.473565 

16 

2.952164 

3.425943 

3.970306 

4.594973 

5.310893 

6.130392 

17 

3.158815 

3.700018 

4.327633 

5.054470 

5.895091 

6.866040 

18 

3.379932 

3.996019 

4.717120 

5.559917 

6.543551 

7.689964 

19 

3.616527 

4.315701 

5.141661 

6.115909 

7.263342 

8.612760 

20 

3.869684 

4.660957 

5.604411 

6.727500 

8.062309 

9.646291 

PRACTICAL  PROBLEMS 

1.  Find,  by  using-  the  table,  the  compound  interest  of  $1050 
for  1  yr.  5  mo.  24  ds.  at  10%,  interest  payable  quarterly. 

2.  Of  $1500  for  7  yrs.  3  mo.  15  ds.,  interest  at  6%,    payable 
semi- annually. 

3.  Of  $2700  for  17  yrs.  7  mo.  7  ds.,  interest  at  7%,    payable 
annually. 

4.  Of  $5400  for  24  yrs.  11  mo.  11  ds.,  at  11%,   interest  pay- 
able annually. 

5.  Of  $12000  for  18  yrs.  8  mo.  6  ds.,   at  10%,   interest  pay- 
able semi-annually. 


Commercial  Paper 

745.  Commercial  Paper  is  the  written  promise  or  request 
to  pay  money. 

746.  There  are  two  classes  of  Commercial  Paper,  viz  : 

I.  PROMISE  TO  PAY  : 

1.  Promissory  Notes. 

2.  Bonds. 

3.  Paper  Currency. 

II.  REQUESTS  TO  PAY  : 

1.  Orders. 

2.  Personal  Drafts. 

3.  Bank  Checks. 

4.  Bank  Drafts. 

5.  Bills  of  Exchange. 

6.  Letters  of  Credit. 

747.  A  Promissory  Note  is  the  written  promise  of  one  or 
more  individuals  to  pay  a  certain  sum  at  a  specified  time. 


Promissory  Note  Payable  on  Demand. 


Promissory  Note  Payable  in  Gold  Coin 


208 


MODERN  BUSINESS  ARITHMETIC 


WL> 


St/  T-X ^L^~  ^(a^^t^^rt^  /C2-x^^f .  ^^^^^C^^U^Z^^A^^r 

/n^  is  /y  ' 


Promissory  Firm  Note  Payable  at  Bank. 


Promissory  Joint  Note  Payable  at  Bank. 

748.  A  Bond  is  the  promissory  note  of  a  government,  state, 
or  corporation. 

749.  Paper  Currency  is  the  promissory  notes  of  the  gov- 
ernment, or  of  a  national  bank,  to  pay  to  bearer  on  demand  the 
sum  specified,  and  is  of  four  kinds,  viz  : 

1 .  National  Treasury  Notes  (  Greenbacks  ) . 

2.  National  Bank  Notes. 

3.  Government  Silver  Certificates. 

4.  Government  Gold  Certificates. 

750.  An  Order  is  the  informal  written  request  of  one  per- 
son upon  another  to  pay  a  third  party  a  certain  sum. 

751.  A  Personal  Draft  is  a  formal  order  and  is  definite 
in  time,  amount,  and  other  conditions. 


COMMERCIAL  PAPER 


209 


Personal  Sight  Draft. 


Personal  Time  Draft 

NOTE — DRAFTS  are  sometimes  called  "  Domestic  Bills  of  Exchange" 
to  distinguish  from  Foreign  Bills  of  Exchange 

752.     A  Bank  C/ieci:  is  an  order  on  a  bank  to  pay  a  certain 
sum  at  sicrht. 


Bank  Check 


210 


MODERN  BUSINESS  ARITHMETIC 


Draft  Form  of  a  Bank  Check 

753.     A  Bank  Draft  is  the  order  of  one  bank  on   another 
bank  to  pay  a  certain  sum  either  at  sight  or  at  a  specified  time. 


'Urtrbnttts  ahlimtal  wnnk 


Bank  Draft 

754.  A  Bill  of  Exchange  is  a  bank  draft  on  a  bank  lo- 
cated in  a  foreign  country. 

755.  A  L/etter  of  Credit  is  a  bill  of  exchange  authorizing 
certain  banks  to  pay  to  the  holder  any  sum  not  exceeding  a  cer- 
tain amount. 


ete 


4^^     Xf< 

^  ~~a5«K    ^"-<^* 

^-"  -^  "^^  &€Z*7'0_.  V^£*T*1»* 
_  _  .   ,_  y^  •      '   ^v^ 

A  Bank  Draft  on  a  Business  House 


COMMERCIAL  PAPER 


211 


756.     A  Cashier's  Check  is  the  check  of  the  cashier  of  a 
bank,  and  when  desired,  is  given  instead  of  currency. 


^~/c, 


Cashier's  Check. 


Another  Form  of  Cashiers  Check. 

757.  A  Certificate  of  Deposit  states  that  the  depositor 
has  a  certain  amount  of  cash  in  the  bank  which  he  may  draw 
out  upon  conforming  with  the  requirements  of  the  certificate. 


Certificate  of  Deposit. 


212  MODERN  BUSINESS  ARITHMETIC 

758.     A  Receipt  is  the  written  acknowledgment  of  the  pay- 
ment of  a  debt  or  of  the  delivery  of  goods. 


Form  of  Receipt. 

759.  An  Indorsement  is  a  writing  on  the  back  of  com- 
mercial paper  for  the  purpose  of  : 

1.  Acknowledging  a  partial  payment. 

2.  Making  the  paper  transferable. 

3.  Guaranteeing  its  payment. 

760.  Negotiable  Paper  is  commercial  paper  that  can  be 
transferred  and  usually  contains  the  words  ' '  to  order, "   or   "to 
bearer. ' ' 

761.  The  Pace  of  the  note  or  draft  is  the  sum  for  which  it 
is  written. 

762.  The  Maker  of  a  note  is  the  one  who  promises  to  pay  ; 
the  one  who  signs  it. 

763.  The  Drawer  of  a  note  is  the  one  who  orders  another 
to  pay ;  the  one  who  signs  it. 

764.  The  Payee  is  the  one  to  whom  the  money  is  to  be 
paid. 

765.  The  Drawee  of  a  draft  is  the  one  who  is  ordered  to 
pay. 

766.  The  Indorser  is  the  one  who  writes  his  name  on  the 
back  of  the  paper. 

767.  Commercial  paper  matures  upon  the  day  it  legally  be- 
comes due.     If  it  becomes  due  upon  Sunday  or  any  other  legal 
holiday,  it  matures  on  the  next  business  day  following. 


COMMERCIAL  PAPER  213 

768.  Three  Days  of  Grace  were  once  granted  by  law,  but 
in  most  states  are  not  now  allowed. 

769.  To  Accept  a  draft  is  to  write  the  word   "accepted" 
with  date  and  signature  of  drawee  across  the  face  of  it.     It  then 
becomes  his  written  promise  to  pay. 

770.  An  Acceptance  is  a  draft  that  has  been  accepted. 

771.  Sight  Drafts    are    payable    on    demand,    and    time 
drafts  are  payable  at  a  specified  time  after  sight. 

772.  To  Honor  a  draft  is  to  pay  it  or  to  accept  it. 

773.  Promissory  Notes  may  be  payable  on  demand  or  at  a 
specified  time.     They  may  be  individual  or  joint  notes,  and  may 
or  may  not  bear  interest. 

774.  The  Legal  Rate  of  the  state  prevails  when  a  note  is 
"  icif/i  interest  "  and  no  rate  specified,  and  all  notes  bear  interest 
after  maturity. 

775.  To  Find    the  Amount    Due  on   Commercial 
Paper. 

Find  the  interest  on  the  face  of  the  paper  for  the  given  time  and 
rate.  rFhe  sum  of  the  interest  and  face  of  the  paper  will  be  the 
amount  due. 

NOTE — To  find  the  time  a  note  WITH  INTEREST  has  to  run,  compute 
the  time  from  the  date  of  the  note  to  the  date  of  settlement.  If  the  note 
is  WITHOUT  INTEREST,  compute  the  time  from  maturity  to  the  date  of. 
settlement. 

EXAMPLE  :  Find  the  amount  June  25,  1908,  of  the  following 
note : 

$720%  Chicago,  III.,  January  10,  1907. 

Nine  months  after  date  I  promise  to  pay  Henry  H.  Howe,  or 
order,  Seven  hundred  twenty  Dollars,  with  interest  at  six  per  cent. 
Per  annum. 

D.  M.   COOK. 

June  25,  1908  =  1908  yr.  6  mo.  25  ds. 

Jan.  10,  1907  =  1907  yr.  1  mo.  10  ds. 

Time  note  has  to  run  =         1  yr.     5  mo.     15  ds. 

$.0875      =  Int.  on  $1.00  for  1  yr.  5  mo.  15  ds. 

720 

63.00  =  Int.  on  $720  for  1  yr.  5  mo.  15  ds. 
720.00  =  Face  of  Paper. 
$783.00  =  Amt.  due,  Ans. 


214  MODERN  BUSINESS  ARITHMETIC 

776.     Find  the  amount  due  at  settlement  of  the  following  : 


$810%  New  York,  N.  Y.,  Apr.  20,  1907. 

One  year  after  date  I  promise  to  pay  J.  E.  Olson  Eight  hun- 
dred ten  Dollars,  with  interest  at  seven  per  cent. 

G.  H.  MOORE. 


Settlement  made  July  1,  1908. 
2. 


$1080%  Eos  Angeles,  Cat.,  Oct.  26,  1905. 

Six  months  after  date  I  promise  to  pay  Henry  Brayton,  or 
order,  Ten  hundred  eighty  Dollars,  with  interest. 

BYRON  R.  MARSH. 


Settlement  made  May  5,  1908.     Legal  rate, 


$420%  San  Francisco,  Cal.,  Apr.  14,  1907. 

One  day  after  date  I  promise  to  pay  E.   P.   Heald,   or  order, 
Four  hundred  twenty  Dollars. 

JOHN  H.  DOE. 


Settlement  made  July  1,  1908. 
4. 


$2000%  Milwaukee,   Wis.,  Nov.  so,  1906. 

Three  months  after  date  I  promise  to  pay  Geo.    W.  Peck,  or 
order,  Tivo  thousand  Dollars,  without  interest. 

W.   C  ROBERTS. 


Settlement  made  December  31,  1907.     Legal  rate,  1%. 
5. 


$642.60  Detroit  Mich  ,  September  i, 

Sixty  days  after  date  we  promise  to  pay  A r land  &  Co-  Six 
hundred  forty-two  6%oo  Dollars,  with  interest  at  eight  per  cent, 
per  annum. 

F.   O.  GARDINER  &  CO. 


Settlement  made  at  maturity. 


COMMERCIAL  PAPER  215 

_6.  __ 

$500%  Cincinnati,  Ohio.,  Feb.  4,  1905. 

One  year  after  date  I  promise  to  pay  P.  R.  Spencer,  or  order, 
Five  hundred  Dollars,  with  interest  at  six  per  cent,  per  annum, 
to  be  paid  semi-annually  ,  and  if  not  so  paid  to  draw  interest  until 
settlement. 

H.  A.  REID. 

Settlement  made  October  25,  1907. 


$3000%  Santa  Rosa,  Cal.,Jan.  1 

Two  years  after  date  I  promise  to  pay  the 

SAVINGS  BANK  OF  SANTA  ROSA 

Three  thousand  Dollars,  with  interest  at  eight  per  cent,  per  an- 
num, payable  quarterly,  and  if  not  so  paid  to  bear  interest  until 
settlement. 

R.  G.  BRACKETT. 

Settlement  made  at  Maturity. 

8.  _  '  _ 

$2400%  Cedar  Rapids,  Iowa,  June  10,  1006. 

Two  years  after  date  I  promise  to  pay  A.  N.  Palmer,  or  order, 
Twenty-  four  hundred  Dollars,  with  interest  at  six  per  cent.  ,  com- 
pounded semi-annually. 

E.  Z.  MARK. 

Settlement  made  at  maturity. 

9.  _  ____ 

$1000%  Stockton,  Cal.,June  17,  1907. 

On  demand  after  date,  at  three  o'clock  p.  m.,  of  that  day,  for 
value  received  I  promise  to  pay  the  order  of  the 

Stockton  National  Bank,  of  Stockton,  Cal. 

One  thousavd  Dollars,  with  interest  from  date  at  the  rate  of  seven 
per  cent,  per  annum  until  paid,  interest  to  be  paid  quarterly, 
and  if  not  so  paid,  to  be  added  to  the  principal  and  bear  the  same 
rate  of  interest  until  paid:  both  principal  and  interest  payable  in 
Gold  Coin  of  the  United  States. 

G.  L.  GILMORE. 

Settlement  made  December  5,  1908. 


216  MODERN  BUSINESS  ARITHMETIC 

10. 


/tf^^ 

W  S 


What  is  due  on  the  above  note  at  maturity,  the  interest  for  the  first 
quarter  having  been  paid? 


Questions  for  Review 


1.  Define  Commercial  Paper  and  classify  its  subdivisions. 

2.  What  is  a  Promissory  Note?     Write  one. 

3.  How  does  a  Bond  differ  from  a  Promissory  Note.- 

4.  Describe  and  classify  the  different  kinds  of  Paper  Cur- 
rency. 

5.  Describe  the  following :     Order.     Personal  Draft.     Bank 
Check.     Bank  Draft.     Bill  of  Exchange.     Letter  of  Credit. 

6.  How  does  a  Cashier's  Check  differ  from  a  Certificate  of 
Deposit  ? 

7.  What  are  Indorsements,  and  for  what  purposes  are  they 
made? 

8.  Define :     Negotiable  Paper.       Maker.      Drawer.      Payee. 
Drawee. 

9.  What  is  meant  by  "Accepting  a  Draft,"  and  what  is  an 
accepted  draft  called  ? 

10.     What  is  meant  by  * '  Honoring  a  Draft  "  ?     By  Legal  Rate  ? 


Partial  Payments 

777.  Partial  Payments  are  payments  in  part  on  a  note, 
bond,  or  other  obligation  to  pay. 

778.  The  Acknowledgment  of  a  partial  payment  is  usu- 
ally made  by  a  writing  on  the  back  of  the  note  and  is  called  an 
Indorsement.       Acknowledgments    of    payments    may    also    be 
written  on  a  separate  sheet  of  paper. 

779.  There  are  two  methods  in  regular  use  in  computing  in- 
terest when  partial  payments  have  been  made,  viz  :  The  "United 
States  Method,"  and  the  "  Merchants  Method." 

780.  The  United  States  Method  is  taken  from  the  de- 
cision of  the  Supreme  Court  of  the  United  States  and  prevails 
when  appeal  is  made  to  the  courts. 

781.  The  Merchants'  Method  is  in  more  common  use 
as  it  is  briefer  and  the  interest  more  readily  computed. 


United  States  Method 

782.     In  computing  interest  by  the  United  States  method,  the 
following  points  must  be  observed  : 

1.  In  computing  time,  find  the  time  by  compound  subtraction 
from  the  date  interest  begins  to  the  time  of  the  first  payment. 

2.  If  the  payment  equals  or  exceeds  the  interest  due,   subtract 
the  payment  from  the  amount  of  the  note  and  treat  this  difference 
as  a  new  principal. 

3 .  //  the  interest  due  is  greater  than  the  payment,  continue  the 
interest  on  the  former  principal  until  such  time  as  the  sum  of  the 
payments  exceeds  the  interest  due,  then  subtract  the  sum  of  the  pay- 
ments from  the  amount,  and  treat  the  result  thus  obtained  as  a  new 
principal. 

4.  Find  the  amount  of  the  last  principal  to  the  date  of  settle- 
ment. 


218  MODERN  BUSINESS  ARITHMETIC 

EXAMPLE  :     Find  the  amount  due  July  1,  1908  : 


Indorsed  as  follows  : 


SOLUTION  : 

Face  of  note,  first  principal  $600.00 

Int.  to  Oct.  16,  1907,  3  mo.  15  ds.  10.50 

Amount  610.50 

Payment  40.50 

Second  principal  $570.00 

Int.  on  2d  prin.  to  Jan.  10,  1908,  2  mo.  24  ds.  7. 93 

Amount  577.98 

Payment  77.9.S 

Third  principal  $500.00 
Int.  on  3d  prin.  to  Apr.  1,  1908,  2  mo.  21  ds.     $6.75 
Int.  on  3d  prin.  to  June  1,  1908,  2  mo.                    5.00 

Amount. 

Sum  of  payments  $5.00  +  $26.75 

Fourth  principal  $480.00 

Int.  to  July  1,  1908,  1  mo.  2.40 

Amount  due  $482.40 


PARTIAL  PAYMENTS 


219 


783.     Find  the  amount  due  at  settlement  of  the  following,  the 
indorsements  of  each  note  will  be  found  on  page  220  : 
1. 


2. 


Settlement  made  at  maturity. 


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What  was  due  at  maturity? 


3. 


What  was  due  January  1,  1608? 


220 


MODERN  BUSINESS  ARITHMETIC 


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PARTIAL  PAYMENTS 


221 


4. 


What  was  due  July  2,  1907? 


5. 


What  was  due  Feburary  29,  1908? 


Merchants'  Method 


i. 


What  was  due  March  10,  1908? 


222 


MODERN  BUSINESS  ARITHMETIC 


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PARTIAL  PAYMENTS  223 

784.  The  Merchants'  Method  of  computing  interest 
when  partial  payments  have  been  made  is  the  one  used  by  most 
banks  when  the  time  to  run  is  less  than  a  year. 

1.  Find  the  amount  of  the  note  or  debt  from  its  date  to  the  time 
of  settlement. 

2.  Find  the  amount  of  each  payment  from  its  date  to  the  time  of 
settlement. 

3.  From  the  amount  of  the  note  or  debt  take  the  sum  of  the 
amounts  of  the  payments,  the  difference  will  be  the  amount  due. 

2.  What  was  due  July  1,  1908  on  a  note  for  $600  bearing  6% 
dated  July  1,  1907,  and  having  the  following  indorsements: 

Sept.  16,  1907,  $100.00 
Nov.  13,  1907,  75.00 
Jan.  10,  1908,  125.00 
April  19,  1908,  $200.00 

3.  What  was  due  on  a  twelve  months'   note  for  $900  dated 
May  10,  1906,  bearing  8%  interest,  and  having  the  following  in- 
dorsements : 

July  1,  1906,  $240.00 

Sept.  10,  1906,  324.00 

Jan.  1,  1907,  180.00 

Mar.  10,  1907,  120.00 

4.  A  note  for  $1200  dated  Sept.    1,    1907,   payable  in  six 
months  with  interest  at  7  %  had  the  following  endorsements : 

October  25,  1907,    $150.00 
Nov.  30,  1907,  300.00 

Jan.  2,  1908,  450.00 

Feb.  12,  1908,  210.00 

What  was  due  at  maturity,  interest  on  payments  computed  for 
the  exact  number  of  days  and  360  days  to  the  year  ? 

5.  Payments  were  made  on  an  interest  bearing  debt  of  $3300 
due  in  one  year  from  June  1,  1906  with  interest  at  9%  as  follows  : 

Sept.  12,  1906,  $300.00 

Jan.  2,  1907,  1000.00 

March  25,  1907,  1000.00 

May  5,  1907,  1000.00 
What  was  due  at  maturity  ? 


224  MODERN  BUSINESS  ARITHMETIC 

HOME  WORK— No.  22 
785.     Solve  the  following  by  Merchants'  Method  : 

1.  Find  the  amount  due  December  31,   1907,   on  a  note  for 
$600  drawing  7%  interest,  dated  Feb.  15,  1907,  and  indorsed  as 
follows:     March  25,  1907,  $150;  June  1,    1907,   $75;    Oct.    10, 

1907,  $100. 

2.  Find  the  amount  due  at  maturity  of  a  note  for  $720  dated 
Jan.  25,  1908,  payable  in  9  months,  with  interest  at  7%,  and  in- 
dorsed as  follows :     March  2,  1908,   $225;   May  5,    1908,   $175; 
June  29,  1908,  $220;  Aug.  1,  1908,  $75. 

3.  A  debt  of  $2100  due  April  5,    1907,  was  paid  off  as  fol- 
lows:    $180  on  May  10,  1907;  $240  on  July  1,    1907;  $645  on 
Aug.  5,  1907  ;  $375  on  Oct.  1,  1907.     What  was  due  December 
31,  1907,  interest  at  6%  ? 

4.  What  is  the  amount  due  on  a  note  for  $855  dated  July  5, 

1908,  due  in  one  year,  and  bearing  interest  at  8%,  and  indorsed 
as  follows:     Nov.   10,  1908,  $210  ;  Jan.   2,    1909,   $150;   March 
25,  1909, '$120;   May  15,1909,  $120;   May  15,  1909,  $100? 

5.  A  bought  a  farm  and  gave  his  note  for  $4500  dated  Sept. 
7,  1907,  with  interest  at  7^%,  payable  one  year  after  date.     If 
the  following  endorsements  were  made,  what  was  due  at  matur- 
ity :     Oct.  17,  1907,  $500;   Nov.  27,  1907,  $500:  Feb.  29,  1908, 
$500;  April  11,  1908,  $500;  June  15,  1908,  $500? 


DISCOUNT 

786.  Discount  is  an  allowance  made  for  the  payment  of  a 
debt  before  it  becomes  due. 

787.  The  Present  Worth  of  a  debt  is  such  a  sum  as  placed 
on  interest  for  the  term  of  discount  at  the  given  rate  will  amount 
to  the  debt. 

788.  The   True  Discount  is  the  difference  between  the 
present  worth  and  the  face  of  the  debt. 

789.  A  Bank  is  an  institution  organized  for  the  purpose  of 
receiving  money  on  deposit,  making  loans,  discounting  commer- 
cial paper,  selling  and  cashing  bills  of  exchange,  making  collec- 
tions, and  in  the  case  of  national  banks,    issuing  a  paper  cur- 
rency. 

790.  Bank  Discount  is  a  deduction  made  by  a  bank  in 
buying  commercial  paper. 

791.  Days   of  Grace   in   states   allowing   the   same   are 
always  considered  when  computing  bank  discount. 

NOTE — In  this  work  no  days  of  grace  are  used  except  when  especially 
mentioned. 

792.  The  Term  of  Discount  is  the  time  from  the  day  of 
discount  to  maturity. 

793.  The  Collection  is  a  sum  charged  by  a  bank  for  mak- 
ing collections  on  commercial  paper.     It  is  always  charged  on 
the  face  of  the  paper. 

794.  The  Pace  of  the  debt  is  the  total  amount  due  at  the 
end  of  the  Term  of  Discount. 

795.  The  Proceeds  of  a  collection  is  the  amount  collected 
less  the  discount,  collection,  protest,  or  other  charges. 

796.  A  Protest  is  a  formal  statement  in  writing  made  by  a 
Notary  Public  giving  legal  notice  to  an  indorser  or  maker  that  a 
note  or  draft  has  not  been  paid  when  due. 


226  MODERN  BUSINESS  ARITHMETIC 

797.  Given,  the  Pace  of  the  Debt,  the  Time,  and  the 

Rate  to  find  the  true  discoimt. 

FORMULA  :     Face  -*-  $1.00  +  (Rate  X  Time)  =  Pres.  Worth. 
Face  —  Pres.  Worth  =  True  Discount. 

EXAMPLE:  What  is  the  true  discount  on  a  bill  of  $284.90 
due  in  90  days,  money  worth  7%  ? 

$284.90  -*•  $1.0175  =  $280,  Pres.  Worth. 
$284.90  —  $280  =  $4.90,   True  Discount. 

798.  Given,  the  Face  of  the  Debt,   the   Time,  and  the 

Rate  to  find  the  bank  discount. 

FORMULA  :     Face  X  Rate  X  Time  =  Bank  Discount. 

EXAMPLE  :  What  is  the  discount  on  a  note  for  $600  due  in  1 
year,  with  interest  at  6%,  discounted  at  bank  for  7  mo.  21  ds. 
at  10%  ? 

$600  X  .06  =  $36,  Int.        $600  +  $36  $636,  Face  of  Debt. 
Int.  on  $636  for  7  mo.  21  ds.  at  10%  =  $40.81,   Bank  Dis. 


PRACTICAL  PROBLEMS 

799.     Solve  the  following  : 

1.  What  is  the  present  worth  of  a  debt  of  $245.04  due  in   3 
mo.  18  ds.,  money  worth  7%  ? 

2.  What  is  the  true  discount  of  a  bill  of  mdse.  amounting  to 
$684.90  due  in  2  mo.  6  ds.  discounted  at  8%  ? 

3.  What  is  the  bank  discount  of  a  note  for  $475  without  in- 
terest, due  in  4  mo.  24  ds.,  discounted  at  6%  ? 

4.  What  are  the  net  proceeds  of  a  note  for  $1150  due  in  1  yr. 
3  mo.  18  ds.,  without  interest,  discounted  at  bank  at  7%  ? 

5.  What  is  the  difference  between  the  true  and  the  bank  dis- 
count of  a  note  for  $1007.60  due  in  11  mo.  27  ds.,  money  worth 
5%? 

6.  A  merchant  bought  a  bill  of  goods  for  $1350  on  90  days 
time,  or  a  cash  discount  of  2%.     Which  was  preferable  and  how 
much,  if  money  at  true  discount  is  worth  7%  ? 


DISCOUNT  227 

7.  An  invoice  of  structural  steel  for  $22500  was  billed  on  6 
months  time,  or  a  discount  of  3%  for  cash  in  30  days.     Which 
would  be  preferable  and  how  much,  to  let  the  bill  run,  or  borrow 
money  at  the  bank  at  8  %  ,  and  pay  cash  ? 

8.  On  Nov.  10.  1907,  I  sold  at  bank  the  following  note  at  S% 
discount  : 

$3000%  Oakland,  Cat.,  July  1,  1907. 

One  year  after  date  I  promise  to  pay    W.  E.   Gibson,  or  order, 
Three  thousand  Dollars  with  interest  at  six  per  cent,  per  annum. 

L.  W.  WATSON. 
Find  net  proceeds. 

9.  I  have  an  account  for  $890.12  that  must  be  settled.     If  I 
borrow  the  money  at  the  bank,  for  how  much  must  my  note  be 
drawn  if  it  is  to  run  5  mo.  15  ds.  discounted  at  8%  ? 

10.     Find  the  proceeds  of  the  following  note  discounted  at  bank 
December  24,  1906,  at  9%  for  time  yet  to  run,  paying  collection 


$5400%  Sacramento,  CaL,  Apiil  1,  1906. 

Two  years  after  date  I  promise  to  pay  Edw'd  Howe,  or  order, 

Fifty  -four  hundred  Dollars  with  interest  at  six  per  cent,  per  annum. 

S.  J.  ROBERTSON. 


Banking  and  Exchange 

800.  A  Bank  is  an  institution  chartered  by  law  to  receive 
deposits,  loan  money,  discount  commercial  paper,  sell  and  cash 
bills  of  exchange,  make  collections,   and  in  the  case  of  national 
banks,  to  issue  bank  bills,  or  national  bank  currency. 

801.  There  are  two  classes   of  banks,   viz:     National  Banks 
and  State  Banks. 

802.  A  National  Bank  is  one  that  is  chartered  under  the 
laws  of  the  United  States  and  has  certain  privileges  not  granted 
to  state  banks. 

803.  A  State  Bank  is  one  that  is  chartered  under  the  laws 
of  the  state  in  which  it  is  located. 

804.  A  Savings  Bank  is  a  bank  which  makes  a  specialty 
of  receiving  deposits,  large  or  small,  on  which  it  pays  interest. 
Banks  of  savings  only,  do  not  do  regular  commercial  business, 
but  loan  their  money  only  on  the  best  real  and  chattel  security. 

NOTE — The  methods  of  CREDITING  INTEREST  on  deposits  in  savings 
banks  are  so  various  that  it  is  needless  to  discuss  the  subject  in  this  work 
except  in  a  general  way. 

805.  Interest  on  Savings  is  credited  monthly,   quarterly, 
or  semi-annually  according  to  the  custom  of  the  bank. 

806.  Interest  on   Withdrawals   is  charged  for  the  re- 
mainder of  the  term  on  the  amount  withdrawn. 

EXAMPLE:  A  deposits  $600,  Jan.  1,  1908,  in  a  savings  bank 
which  pays  4%  interest  on  all  deposits.  Feb.  1,  1908,  he  draws 
out  $150,  and  on  March  1,  1908,  $150.  Find  amount  in  bank 
at  end  of  the  first  quarterly  period. 

SOLUTION  : 

January  1,  A's  deposit  $600.00 

January  1,  3  month's  interest  to  April  1  6.00 

Total  amount  of  deposit  and  interest  $606.00 

February  1,  1st  withdrawal  $150.00 

February  1,  interest  to  April  1  1.00 

March  1,  2d  withdrawal  150.00 

March  1,  interest  to  April  1  .50 

Total  withdrawals  and  interest  301.50 

Balance  in  bank  $304.50 

NOTE — The  foregoing  method  is  only  one  of  several  but  is  considered 
one  of  the  latest  and  best  in  computing  interest  on  savings  accounts. 


BANKING  AND  EXCHANGE  229 

807.  To  find  the  amount  due  on  a  savings  account,  subtract  the 
sum  of  the  amounts  of  the  withdrawals  at  the  end  of  the  term  from 
the  sum  of  the  amounts  of  the  deposits  to  the  same  time. 

808.  Overdrafts  are  allowed  by   some   banks   to   special 
patrons  who  are  charged  a  higher  rate  of  interest  than  on  ordi- 
nary loans. 

809.  Most  banks  charge  ten  or  twelve  per  cent,   on  over- 
drafts, the  charge  being  made  on  the  average  amount  checked 
out. 

EXAMPLE  :  A's  overdraft  was  $3000  on  July  1st,  and  for  5 
days  thereafter.  On  the  7th  he  deposited  $1000.  On  the  12th 
checks  came  in  against  him  for  $2400.  On  the  21st  $4500  more 
was  checked  out.  On  the  27th  he  put  in  $2900.  Charging  12%, 
what  will  be  the  interest  on  his  overdrafts  for  July  ? 

$3000  for  6  days  =  $18000  for  1  day 
2000  for  5  days  =  10000  for  1  day 
4400  for  9  days  =  39600  for  1  day 
8900  for  6  days  =  53400  for  1  day 
6000  for  5  days  =  30000  for  1  day 
Total  overdraft,  $151000  for  1  day 


so  300 


$151000          Or, 

1  day  $151000   .    ^    _  tf.n  77   ,   , 

.&%  ---30  — $50.33,  Int. 


Int.,  $50.33 


810.  To  find  the  interest  on  overdrafts ,  divide  1%   of  the  total 
amount  of  the  daily  overdrafts  by  30  if  for  12% ,  by  36  if  for  10% , 
by  40  if  for  9% ,  and  by  45  if  for  8% ,  etc. 

811.  The  Profits  of  a  bank  are  distributed  to  three  differ- 
ent accounts  : 

1.  To  the  Surplus  Fund. 

2.  To  the  Dividend  Account. 

3.  To  the  Undivided  Profits. 

812.  National  Banks,  before  declaring  their  regular  semi- 
annual dividends,  are  required  to  place  10%   of  their  profits  in 
the  Reserve  Fund  until  it  equals  20%  of  their  capital  stock. 


230  MODERN  BUSINESS  ARITHMETIC 

EXAMPLE  :     If  the  net  profits  of  a  National  Bank  whose  capi- 
tal stock  is  $100000  are  $5280,  they  may  be  divided  as  follows  : 

10%  of  $5280  $528,  carried  to  Surplus  Fund. 

4%  on  Cap.  Stock  =      4000,  carried  to  Dividend  Account. 
Remainder  =      750,  carried  to  Undivided  Profits. 

$5278,  Total  Profits. 

813.  Exchange  is  the  process  of  making   payments  at   a 
distance  without  actually  sending  the  money. 

814.  Exchange  is  one  of  the  functions  of  a  bank  in  receiving 
the  money  to  be  paid  and  by  issuing  a  Draft  or  Bill  of  Exchange 
on  its  correspondent  in  the  distant  city. 

815.  Collection  and  Exchange  are  the  charges  made  by 
a  bank  for  making  collections  on  Commercial  Paper,  and  for  is- 
suing. Drafts  and  Bills  of  Exchange. 

816.  Domestic  Exchange  is  the  exchange  between  cities 
of  the  same  county. 

817.  Foreign  Exchange  is  the  exchange  between  cities 
of  different  countries. 

818.  The  Charges  on  domestic  exchange  are  usually  com- 
puted at  a  certain  rate  per  cent,   on  the  face  of  the  draft,   and 
that  on  foreign  exchange  depends  upon  the  market  quotations 
which  may  be  either  above  or  below  the  intrinsic  value. 

NOTE— The  intrinsic  value  of  the  £  is  $4.8665  ;  of  the  franc,  $.193  ;  of 
the  mark,  $.2385. 

French  quotations  at  5.20  means  that  5i  francs  equal  $1  in  United 
States  money. 

German  quotations  at  95  means  that  4  marks  equal  $.95  in  United 
States  money. 


PRACTICAL  PROBLEMS 

819.     Solve  the  following  : 

1.     Find  the  exchange  on  a  draft  on  New  York  for  $1244  at 


2.  A  bank  charged  }i%  on  a  draft  for  $760.     What  was  the 
cost  of  the  draft  ? 

3.  The  exchange  on  a  draft  on  Boston  was  $9.15.  -   If  the 
rate  was  /^  % ,  what  was  the  cost  of  the  draft  ? 


BANKING  AND  EXCHANGE  231 

4.  I  paid  my  banker  $256.64  for  a  draft  on  San  Francisco. 
If  the  rate  of  exchange  was  l/i  % ,  what  was  the  face  of  the  draft? 

5.  What  will  a  ,£600  draft  on  London  cost  if  the  quotation  is 
4.87  and  %%  exchange  is  added? 

6.  Find  the  cost  of  a  draft  on  Paris  for  1573.20  francs  if  the 
market  quotation  is  5.17/4. 

7.  I  bought  a  draft  on  Berlin  for  840  marks,  when  the  mar- 
ket quotation  was  96.     What  did  it  cost  me  ? 

8.  A  national  bank  has  a  capital  of  $100000.     If  its  net  prof- 
its are  $7325.40,  and  it  declares  a  dividend  of  5%,  what,  amounts 
should  be  placed  in  the  Surplus  Fund,  in  the  Dividend  Account, 
and  in  the  Undivided  Profits  Account  ? 

9.  A  bank  with  a  Capital  Stock  of  $150000,  a  Surplus  Fund 
of  $12500,  an  uncollected  Subscription  Account  of  $30000,  and 
whose  net  profits  at  the  close  of  the  year  are  $18345.20,  declares 
the  highest  whole  rate  per  cent,  dividend  possible  on  paid  up 
stock  after  placing  10%   of  the  profits  in  the  Surplus  Fund. 
What  are  the  total  Surplus  Fund,  the  Rate  of  Dividend,  and  the 
Undivided  Profits  ? 

10.  What  will  be  A's  balance  at  the  end  of  a  year  in  a  savings 
bank  that  allows  4%  interest  on  all  balances  and  deposits,  and 
which  charges  interest  on  all  withdrawals  for  the  remainder  of 
each  quarter?  July  1,  1907,  deposited  $800;  August  16,  de- 
posited $400 ;  September  1,  withdrew  $200;  November  1,  de- 
posited $500;  December  24,  deposited  $1000.  February  5,  1908, 
withdrew  $450;  April  1,  deposited  $300;  April  18,  withdrew 
$100  ;  May  10,  withdrew  $150  ;  June  1,  deposited  $120. 


232  MODERN  BUSINESS  ARITHMETIC 

HOME  WORK-NO.  23 

1.  Bought  a  draft  on  New  York  for  $2320,  paying  exchange 
at  %  % .     What  did  the  draft  cost  me  ? 

2.  A   Chicago  merchant  bought  a  draft  on  San  Francisco, 
paying    exchange  $3.78  at   $%.     What  was  the   face    of   the 
draft  ? 

3.  A  draft  on  Chicago  cost  me  $430.11.     If  the  exchange 
was  $1.71,  what  was  the  rate  charged? 

4.  I  paid  $8502.30  for  a  draft  on  St.   Louis.     If  the  rate  of 
exchange  was  }4  % ,  what  was  the  face  of  the  draft  ? 

5.  What  will  a  draft  on  Liverpool,   England,    for  ^720  cost 
when  the  exchange  is  the  intrinsic  value  plus  >£  %  ? 

6.  What  should  a  draft  on  Berlin  for  2500  marks  cost  if  the 
rate  of  exchange  is  95  ? 

7.  A  traveler  bought  a  draft  on  Berlin  for  6228  marks,   pay- 
ing $1200  for  the  same.     What  was  the  market  quotation  ? 

8.  The  net  profits  of  a  National  Bank  are  $14255.60.     If  the 
capital   stock    is  $150000,    and    the    subscription  $50000,   what 
should  be  the  undivided  profits  after  allowing  for  surplus  fund 
and  declaring  a  dividend  of  10%  ? 

9.  Jan.  1,  1907,  A  deposits  $1200  ;  Jan.    21,   $400;  Feb.   10, 
$200;   March  15,  $150.     If  he  withdraws  $500  Feb.  1,  and  $600 
Mar.  1,  what  will  be  his  balance  Apr.  1,  in  a  savings  bank  that 
pays  4%  interest  ? 

10.  What  would  be  the  balance  of  the  above  Apr.  1,  1907,  if 
simple  interest  was  allowed  on  the  exact  amount  in  the  bank  for 
the  number  of  days  it  remained  unchanged  ? 


Equation  of  Payments 

820.  Equation  of  Payments  is  the  process  of  finding 
the  time  when  several  sums  due  at  different  times  may  be  paid 
without  loss  to  payer  or  payee. 

821.  The  quantities  considered  are  : 

1 .  The  Items  Charged. 

2.  The  Focal  Date. 

3.  The  Terms  of  Credit. 

4.  The  Products  for  a  unit  of  time. 

5.  The  Average  term  of  credit. 

6.  The  Equated  Date. 

822.  The  Items  Charged  are  the  several  amounts  to  be 
paid. 

823.  The  Focal  Date  is  a  fixed  date  from  which  time  is 
reckoned.     The  earliest  or  latest  date  is  most  convenient,   al- 
though an}7  date  may  be  used  for  the  focal  date. 

824.  The  Terms  of  Credit  are  the  intervals  of  time  from 
the  focal  date  to  the  date  each  item  is  due. 

825.  The  Products  are  found  by  multiplying  each  item  by 
its  term  of  credit. 

826.  The  Average  Term  of  Credit  is  found  by  dividing 
the  sum  of  the  products   by  the  sum  of  the  items. 

827.  The  Equated  Date  is  the  date  when  all  the  bills  may 
be  paid  in  equity  to  both  debtor  and  creditor.     It  is   found  by 
computing  the  average  term  of  credit  from  the  focal  date. 

828.  An  Account  is  a  written  statement  of  charges  and 
credits  together  with  the  date  and  time  of  credit  allowed  each 
item . 

829.  To  Average  an  Account  is  to  find  the  time  when 
an  account  may  be  settled  in  equity  to  both  debtor  and  creditor. 

830.  Equation  of  payments  and  averaging  accounts  are   used 
only  by  wholesalers,  jobbers,  manufacturers,  and  large  concerns 


234  MODERN  BUSINESS  ARITHMETIC 

where  the  amounts  are  large  and  interest  on  overdue  balances  is 
demanded. 


CASE  I 

831.  To   find   the  Average  Term  of  Credit    and    the 
Equated  Date. 

1.  Multiply  each  item  by  its  term  of  Credit ',  and  divide  the  sum 
of  the  products  by  the  sum  of  the  items.      The  quotient  is  the  aver- 
age term  of  credit. 

2.  Compute  the  average  term  of  credit  from  the  focal  date  to 
find  the  equated  date. 

EXAMPLE:  I  bought  goods  Jan.  1,  1907,  as  follows:  $400 
on  2  mo.,  $600  on  3  mo.,  and  $800  on  4  mo.  What  is  the  aver- 
age term  of  credit  and  the  equated  date  ? 

The  use  of  $400  for  2  mo.  =  $800  for  1  mo. 
600  for  3  mo.  =  1800  for  1  mo. 
800  for  4  mo.  =  3200  for  1  mo. 

Total  Items,  $1800  $5800,  Total  Products. 

$5800*H-  $1800  =  3%  mo.,  Average  term  of  Credit. 
3%  mo.  after  Jan.  1,  1907  =  Apr.  8,  1907,  Equated  Date. 

832.  Solve  the  following  : 

1.  The  interest  on  $50  for  8  mo.  equals  the  interest  on  $1  for 
how  many  months  ?     On  how  many  dollars  for  2  mo.  ?     Analyze 
carefully. 

2.  The  interest  on  $200  for  6  mo.,   and  on  $400  for  4  mo. 
equals  the  interest  on  $1  for  how  many  months  ?     On  how  many 
dollars  for  7  mo.  ? 

3.  If  I  borrow  $300  for  4  mo.,  for  how  many  months  shall  I 
lend  $200  to  equalize  the  interest  ? 

4.  If  John  borrows  from  James  $800  for  7  mo.,   what  sum 
should  John  lend  James  for  4  mo.  to  equalize  the  obligation  ? 

5.  Find  the  average  term  of  credit  of  $500  due  in  4  mo.,  $750 
due  in  3  mo.,  and  $1000  due  in  2^2  mo. 

6.  I  owe  $140  due  in  2  mo.,  $240  due  in  3  mo.,  $240  due  in 
1  mo.     When  can  I  pay  them  all  in  equity  with  a  single  check? 


EQUATION  OF  PAYMENTS 


235 


7.  On  a  debt  of  $2800  due  in  6  mo.  from  Feb.   1,  the  follow- 
ing payments  were  made  :     May  1,  $500  ;  July  1,   $600;    Sept. 
1,  $1200.     When  is  the  balance  due? 

8.  Find  the  average  term  of  credit  and  the  equated  date  of 
payment  from  July  1,  1908,  of  $450  due  in  30  ds.,   $300  due  in 
60  ds.,  and  $750  due  in  90  ds. 

9.  Sold  A.  J.  Rutherford  goods  as  follows:     June  1,   1908, 
$250  on  2  mo.  credit;  July  15,  $300  on  3  mo.  credit;  Aug.   10, 
$400  on  4  mo.   credit;    September   12,   $600  on   2  mo.   credit. 
What  is  the  average  term  of  credit  and  the  equated  date  ? 

10.  I  bought  merchandise  as  follows:  Sept.  15,  1907,  $100 
on  30  ds.  ;  Oct.  10,  1907,  $275  on  2  mo.  ;  Nov.  15,  1907,  $750 
on  90  ds.  ;  Dec.  20,  1907,  $240  on  60  ds.  ;  and  Jan.  15,  1908, 
$300  on  30  ds.  What  was  due  on  this  account  March  1,  1908, 
if  no  payments  had  been  made?  Money  worth  8%. 


CASE  II 

833.    To  find  the  Equated  Date  and  the  Cash  Balance 

of  an  Account  Current,  or  of  an  Account  Sales. 

PRODUCT   METHOD 

1.  Find  the  date  each  item  is  due,  both  debits  and  credits. 

2.  Multiply  each  item  by  the  number  of  days  from  the  focal  date 
to  the  date  it  is  due. 

3 .  Divide  the  difference  of  the  sums  of  the  products  by  the  bal- 
ance of  the  items,  the  result  is  the  average  term  of  cr-edit. 

4.  If  the  balances  of  items  and  products  are  both  debits  or  both 
credits,  the  equated  date  is  found  by  reckoning  forward  from  the 
focal  date  ;  if  one  is  a  debit  and  the  other  a  credit,  the  equated  date 
is  found  by  reckoning  backward  from  the  focal  date. 

EXAMPLE  :     Find  the  equated  date  of  paying  the  balance  of 
the  following  account. 

Dr.  B.  L.  Trowbridge  Cr. 


1908 

1908 

Jan. 

10 

Mdse.  net 

80000 

Feb. 

15 

Draft  30  ds. 

400 

IK) 

Feb. 

2 

Mdse.  2  mo. 

50000 

Mar. 

5 

Note  60  ds.  (int.) 

600 

00 

Mar. 

12 

Mdse.  3  mo. 

120000 

Apr. 

10 

Note  90  ds. 

May 

4 

Mdse.  4  mo. 

80000 

(no  int.)  900 

00 

236 


MODERN  BUSINESS  ARITHMETIC 


Jan.  10  $800  X 


Mar.  16  $400  X  66  =  26400 


Apr.  2   500  X  83  =   41500  Mar.  5   600  X  55  =  33000 

June  12  1200  X  154  ==  184800  July  9    900  X  181  ==  162900 

Sept.  4   800  X  238  =  190400  $1900         222300 
$3300 


1900 
$1400 


416700 
222300 
)  194400  ( 139.  ds. 


May 


Balance,  $1400,  due  139  days  from  January  10,    1908. 
28,  1908,  equated  date. 

834.  The  Interest  Method  may  be  used  in  finding  the 
equated  date  and  cash  balance  as  follows  : 

1.  Find  the  time  of  each  item  from  the  focal  date,  as  in  the  pro- 
duct method,  and  compute  the  interest  at  i%  per  month  on  each 
item. 

2.  Divide  the  balance  of  the  total  debit  and  the  total  credit  in- 
terests by  the  interest  on  the  balance  of  items  for  one  month  at  i%. 
The  result  will  be  the  average  term  of  credit. 

NOTE — When  a  time  draft  or  a  note  without  interest  is  an  item  of  an 
account,  the  time  of  such  credit  ends  with  the  maturity  of  the  draft  or 
note.  If  the  note  draws  interest,  no  time  of  credit  is  allowed  on  that 
item. 


PRACTICAL  PROBLEMS 

835,     Find  the  equated  date  of  the  following 

1. 

Dr.  A.  C.  Jones 


Cr. 


1907 

1907 

June 

1 

Mdse. 

900 

00 

Aug. 

1 

Cash 

500 

00 

July 

1 

Mdse. 

400 

00 

Sept. 

1 

Cash 

700 

00 

Sept. 

1 

Mdse. 

1200 

00 

Nov. 

1 

Cash 

1000 

00 

Oct. 

1 

Mdse. 

1600 

00 

2. 
Dr.                                     $.  A.  Mills                                     Cr. 

1908 
Jan. 
Jan. 
Mar. 
Mar. 

10 
30 
5 
25 

Mdse.  60  ds. 
Mdse.  60  ds. 
Mdse.  60  ds. 
Mdse.  60  ds. 

800 
600 
400 
700 

00 
00 
00 
00 

1908 
Feb. 
Feb. 
Apr. 

1 
29 
1 

Cash 
Cash 
Cash 

500 
500 
500 

00 
00 
00 

3. 
Dr. 


EQUATION  OF  PAYMENTS 


W.  W.  Willis 


237 


Cr. 


1907 

• 

1907 

Aug. 

1    Mdse.  net 

240 

00 

Sept. 

15 

Cash 

300 

00 

Sept. 

1,  Mdse.  60  ds. 

180 

00 

Oct. 

15 

Cash 

20000 

Oct.  ;  1    Mdse.  30  ds. 

450 

00 

4. 
Dr. 


B.  F.  Strong 


Cr. 


1908 

1908 

Mar. 

15 

Mdse.  3  mo. 

800 

00 

May 

10 

Cash 

400 

oo 

Apr. 

3 

Mdse.  4  mo. 

900 

00 

July 

1 

Note  (with  int.) 

500 

00 

May 

10 

Mdse.  6  mo. 

1200 

00 

Aug. 

15 

Cash 

600 

00 

5. 
Dr. 


M.  I.  Pronini 


Cr. 


1907 

1907 

Aug. 

5 

Mdse.  90  ds. 

650 

00 

Oct. 

1 

Cash 

500 

00 

Sept. 

10 

Mdse.  30  ds. 

437 

50 

Nov. 

1 

Cash 

400 

0(7 

Nov. 

1 

Mdse.  60  ds. 

277 

50 

Dec. 

15 

Note  60  ds. 

Dec. 

1 

Mdse.  30  ds. 

320 

00 

(no  int.) 

600 

00 

HOME  WORK-NO.  24 

1.     Find  the  equated  date  and  cash  balance  Dec.   3,    1908,   of 
the  following,  allowing  interest  at  8%  : 


Dr. 


Robison  &  Shirley 


Cr. 


1908 

1908 

Jan. 

5 

Mdse.  4  mo. 

1500 

00 

Feb. 

5 

Mdse.  4  mo. 

600 

00 

Jan. 

15 

Mdse.  3  mo. 

1200 

00 

Mar. 

1 

Cash 

1500 

00 

Apr. 

1 

Mdse.  60  ds. 

2800 

00 

Mar. 

24 

Draft  30  ds. 

3000 

00 

Apr. 

30 

Mdse.  30  ds. 

2000 

00 

Apr. 

15 

Cash 

1000 

00 

2.     Average  the  following,  and  find  the  amount  due  Nov.   7, 
1908,  interest  at  6%  : 


Dr. 


Hawes  &  Gil  more 


Cr. 


1908 

1908 

I 

Apr. 

1 

Cash  advanced 

250 

00 

Mar. 

10'   Mdse.  4  mo. 

500 

00 

Apr. 
May 

15 
10 

Freight  charges 
Freight  charges 

42 
25 

25 

75 

Apr. 
May 

i;   Mdse.  90  ds. 
15    Mdse.  60  ds. 

400 
600 

(M) 
(M) 

238 


MODERN  BUSINESS  ARITHMETIC 


3.     Find  the  amount  due  Aug.    23,    1908,   bank  discount  al- 
lowed on  balance  at  7  % . 


Dr. 


.  W.  Scarlett  &  Son 


Cr. 


1908 

1908 

June 

1 

Mdse.  30  ds. 

150 

00 

June 

15 

Cash 

200 

00 

11 

10 

Mdse.  net 

312 

50 

July 

1 

Draft  30  ds. 

300 

00 

21 

Mdse.  60  ds. 

475 

50 

" 

15 

Cash 

250 

00 

July 

1 

Mdse.  60  ds. 

321 

75 

Aug. 

1 

Note  60  ds.  on  int. 

500 

00 

15 

Mdse.  30  ds. 

46225 

4.  Average  the  following  Account  Sales ;  find  when  the  net 
proceeds  will  be  due,  and  find  the  amount  required  to  liquidate 
the  account  on  June  30,  1908,  money  being  worth  8%. 


TAI,BOT  J.  POWERS  COMPANY 

Produce  and  Commission 


San  Francisco,  Cal.,         June  21,  1908 

E.   C.  ATKINSON  &  COMPANY, 

Sacramento,  Cal. 

We  render  you  an  Account  Sales  of  your  consignment  of: 
2412  doz.  Eggs 

Received       May  1,  1908. 


1908 

SAI/ES  : 

May 

3 

720  doz.  Eggs           .20 

« 

18 

540   "    "            .22 

June 

12 

360   "    "   -         .23 

« 

20 

792   "    "            .21 

CHARGES: 

May 

1 

Freight 

41 

20 

it 

1 

Cartage 

14 

30 

« 

21 

Storage  and  Insurance 

13 

50 

Commission,  10^  on  sales 

## 

## 

Net  Proceeds 

**•* 

** 

NOTE- -The  date  of  the  commission  is  found  by  averaging  the  sales. 


EQUATION  OF  PAYMENTS 


239 


5.  Average  the  following  Account  Sales,  find  when  the  net 
proceeds  will  be  due,  and  find  the  amount  required  to  liquidate 
the  account  on  June  10,  1908,  money  being  worth  8%  : 


Hollman,  Kinnard  &  Company 

COMMISSION  MERCHANTS 

Chicago,  111.,  April  21,  1908. 

C.  WESTON  CLARK, 
Los  Angeles,  Cal. 

Dear  Sir  :     We  render  you  an  Account  Sales  of  your  consignment  of: 

600  boxes  of  Oranges 

Shipped  via   S.  P.  and  C.  B.  &   Q.  R'y.        Received    March  2,  '08. 

1908 

SALES: 

Mar. 

3 

4 
5 
12 
15 
20 

80     bxs.  Wash.  Navels        90  's 
45       "          "           "            126'  s 
36       "          "           "            ISO's 
120     "      Merced  Sweets   176'  s 
204    "     do.  (on  60  days)  200'  s 
204    "  Tangerines  (on  30  days) 

2 
2 
2 
2 
2 
1 

25 
50 
50 
40 
75 



— 

CHARGES  : 

Mar. 
t  ( 

2 
20 
18 

12 

Freight 
Storage  and  Insurance 
Guaranty 
Cash  advanced 
Commission,  8/6 

124 
33 
31 
500 

75 
50 
65 

Statements  and  Balance  Sheets 


836.     A  Statement  is  an  itemized  schedule  of  the  resources 
and  liabilities  of  any  firm  or  corporation. 

Statement 


837.     By  Resources  is  meant  all    available   properties   or 
values . 


STATEMENTS  AND  BALANCE  SHEETS 


241 


838.  By  Liabilities  is  meant  the  debts  or  obligations  to 
pay. 

839.  A  Trial  Balance  is  a  schedule  showing  the  debit  and 
the  credit  footings  of  the  ledger  accounts  of  a  business. 

Trial  Balance 


NOTE — It  will  be  .noticed  in  the  above  that 
equals  the  sum  of  the  liabilities. 


the  sum  of  the  resources 


242 


MODERN  BUSINESS  ARITHMETIC 


840.  A  Balance  Sheet  consists  of  a  Trial  Balance  together 
with  a  detailed  statement  showing  the  Loss  or  Gain,  the  Inven- 
tories, and  the  Present  Worth  of  a  business. 


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Q  \3  «^ 

*  >  ^ 

S  *  «* 


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<*  Ns 


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STATEMENTS  AND  BALANCE  SHEETS  243 

841.  The  Present  Worth  of  a  business  is  the   difference 
between  the  sums  of  its  Resources  and  Liabilities. 

842.  The    Net    Investment    or    Working  Caital   is    the 
amount  invested. 

843.  An  Inventory  is  a  list  of  goods  or  chattels  on  hand. 
The  word  inventory  is  also  applied  to  a  class  of  unpaid  items  ; 
as,  unpaid  rent,  interest  payable,  etc.,  called  liability  inventories. 

844.  Capital  Stock  is  the  total  sum  which  a  concern  may 
invest  as  its  working  capital. 

845.  Subscriptions  are  the  amounts  promised  by  the  sub- 
scribers to  make  up  the  working  capital. 

846.  Treasury  Stock  is  the  unsubscribed  capital  stock  of 
a  company.     It  is  the  difference  between  the  entire  capital  stock 
and  the  total  subscriptions. 

847.  To  find  the  Present  Worth,  the  Loss  or  Gain,  or 
any  Resource  or  Liability  required. 

1.  From  the  sum  of  the  Resources  subtract  the  sum  of  the  Lia- 
bilities, the  result  is  the  Present  Worth. 

2.  The  difference  between  the  Net  Investment  and  the  Present 
Worth  is  the  Loss  or  Gain. 

3.  The  difference  between  the  Resources  and  the  Liabilities,   in- 
cluding the  Present  Worth,  will  be  the  missing  Resource  or  Liabil- 
ity. 

•  4.  To  find  the  Gain  or  Loss  on  merchandise,  or  any  other  prop- 
erty account,  take  the  difference  between  the  total  debits  and  the  sum 
of  the  inventory  and  the  total  credits  of  the  account. 


PRACTICAL  PROBLEMS 
848.     Solve  the  following : 

1.  Separate  A's  resources  from  his  liabilities,  and  find  his 
present  worth  from  the  following:  Cash  on  hand,  $1974.74; 
Merchandise,  $3777 ;  Bills  Receivable,  $750 ;  Bills  Payable, 
$1155 ;  Furniture  and  Fixture  inventory,  $225.  A  owes  I.  J. 
King  on  account  $250.  M.  N.  Long  owes  A  on  account  $90. 


244  MODERN  BUSINESS  ARITHMETIC 

2.  If  A 's  merchandise  purchases  amounted  to  $5659.50,   his 
sales,    $2427.50,    and    his    unsold    stock,   $3777,   what  was  the 
gain  on  his  merchandise  ? 

3.  Briggs's  net  investment  was  $19000.     His  resources  at  the 
close  of  the   year   were    as    follows:     Merchandise,    $1840.20; 
Cash,  $4250  ;   Bills  Receivable,  $520  ;  Real  Estate,  $12000  ;  Store 
Fixtures,  $580.25;  Accounts  Receivable,  $3849.75.    His  liabilities 
were:     Bills    Payable,     $275.25;    Accounts  Payable,  $1942.60. 
Find  his  present  worth  and  net  gain. 

4.  Anderson's  statement  of  losses  and  gains  is  as  follows  : 
MERCHANDISE:     Sales,  $4967.20.     Inventory,  $1825.60.     Pur- 
chases, $5435.40.     STOCKS:     Cost,  $884.     Sales,   $928.     None 
on  hand.     REAL  ESTATE  :     Cost,  $12000.     Income,  $450.     In- 
ventory, $12200.    FURNITURE  AND  FIXTURES  :     Cost,  $320  ;  In- 
ventory, $280.     EXPENSE  :     General,  $320.     INTEREST  :     Paid, 
$122.40.      Received,   $245. 80.      What  was  his  net  loss   or    net 
gain? 

5.  E.  Wyckoff  &  Co.'s  statement  at  the  close  of  the  year  is 
as  follows  :      Cash  on  hand,   $84500  ;    Merchandise    inventory, 
$7246.50;    Bills  Receivable,  $1200;  Bills  Payable,  $320  ;   Mort- 
gages Payable,  $1000  ;   Interest  Receivable,  $15.80  ;   Interest  Pay- 
able, $35.40;    Accounts  due  the  firm,  $2765.75;  Accounts  due 
others,  $875  ;  due  E.  Wyokoff,  private  account,  $750  ;  Rent  un- 
paid, $200;   Insurance,  prepaid  $27.50.     Find  the  firm's  present 
worth. 


HOME  WORK-NO.  25 

1.  The  following  are  the  assets  and  liabilities  of  Heitman  & 
Hadrich  at  the  close  of  the  year  :  Cash  overdraft,  $1250  ;  Cash 
in  safe,  $245.50;  Merchandise  inventory,  subject  to  10%  dis- 
count, $7324 ;  Notes  Receivable,  subject  to  4%  discount,  $796.25  ; 
Notes  Payable,  $600 ;  Doubtful  Accounts  Receivable,  subject  to 
40%  discount,  $480;  Real  Estate,  $12450;  Mortgage  on  same, 
$5000;  Books,  Stationery,  etc.,  $184.50;  Fuel  and  Feed  on  hand, 
$97.50  ;  Teams  and  Wagons,  $685  ;  Accounts  Receivable,  $9450  ; 


STATEMENTS  AND  BALANCE  SHEETS  245 

Accounts  Payable,  $4155.65.     What  is  the  present  worth  of  each 
if  Heitman's  share  is  double  that  of  Hadrich? 

2.  Find  the  loss  or  gain  of  the  L,.  Kelch  Company  from  the 
following:     Merchandise  inventory,  Jan.   1,    1907,   $5840;  Mer- 
chandise purchases,  $22764.25,  less  rebates  and  returns,  $324.10; 
present    Merchandise    inventory,   Jan.    1,   1908,  $8354.25;  total 
sales,  $25498.69,  less  rebates  and  returns,  171.40;  Furniture  and 
Fixtures  bought,  $276.80;   Furniture  and  Fixtures  inventory, 
$260;  Clerks'  Salaries,  $1225;  Advertising,  $400. 

3.  F.  B.  Bill  &  Co.'s  trial  balance  is  as  follows  :     Cash  deb- 
its,   $21465.40;    Cash  credits,   $19326.10;    Merchandise  debits, 
$34596.50;  Merchandise  credits,  $28976.15;  Accounts  Receivable, 
debits,    $16350;    Accounts  Receivable,  credits,  $14366.25  ;    Ac- 
counts  Payable,    debits,  $  2854.10;    Accounts  Payable,  credits, 
$5820  ;  Interest  and  Discount,  debit  balance,  $426.30;  Store,  lot, 
and  building,  $3000  ;   Mortgage  on  same,  $1000  ;  Insurance  paid, 
$46.80;  Expenses  paid,  $1640.     If  10%  discount  is  allowed  on 
net  balances  due  the  firm,  and  the  merchandise  on  hand  amounts 
to  $11438.90,  what  is  the  net  loss  or  gain,  and  what  is  the  firm's 
present  worth  ? 

4.  A  is  employed  by  a  firm  to  sell  sewing   machines   at   a 
weekly  salary  of  $25.     He  is  given  $32  in  cash,  and  $312.40  in 
merchandise  to  start  with.     His  sales  for  the  week  amounted  to 
$288.60,  and  he  buys  and  receives  merchandise  valued  at  $128. 75. 
If  he  returns  $244.45  worth  of  merchandise  to  the  firm,   did  the 
firm  gain  or  lose  on  his  week's  work,  and  how  much  ? 

5.  I  engaged  with  the  Wiley  B.  Allen  Piano  Company  to  sell 
pianos  at  a  monthly  salary  of  $175  and  expenses.     They  gave 
me  pianos  valued  at  $5240,  cost  price,  and  $100  expense  money 
to  start  with.     My  report  at  the  end  of  the  first  month  was  as 
follows  :     Piano  sales  for  cash,  $2160  ;  piano  sales  on  account, 
$1860  ;  second-hand  pianos  taken  in  trade  valued  at  $490  ;  addi- 
tional new  pianos  received  from  the  firm,  $1200 ;  rent  paid  in 
cash,  $50 ;    stenographer's  service,  $15 ;  hauling,   freight,   and 
express,  $27.25  ;  pianos  in  stock  unsold,  valued  at  $3450.     Did 
the  firm  gain  or  lose,  and  how  much  ? 


PARTNERSHIP 


849.  Partnership  is  the  association  of  individuals  for  the 
purpose  of  transacting  business. 

850.  The  Firm  Name  is  the  title  by  which  any  firm,  com- 
pany, house,  or  concern  is  known. 

851.  The  Capital  is  the  money,   property,   or  other  assets 
.invested. 

852.  Net  Capital,  or  present  worth,  is  the  excess  of  the 
assets  over  the  liabilities. 

853.  Net  Insolvency  is  the  excess  of  the  liabilities  over 
the  assets. 

854.  Partners  are  the  individuals  composing  the  firm  or 
company. 

855.  Partners  are  oifonr  kinds,  viz  : 

1.  Actual  and  known  partners. 

2.  Limited  partners. 

3.  Siknt  partners. 

4.  Nominal  partners. 

856.  Actual  Partners  are  those  who  contribute  to  the 
capital  stock  and  whose  names  are  made  known  to  the  public 
generally. 

857.  l/imited  Partners  are  those  whose  liabilities  are  re- 
stricted to  the  value  of  the  shares  which  they  hold. 

858.  Silent  Partners  are  those  whose  names  do  not  ap- 
pear in  the  firm  title  but  who  share  in  the  profits  of  the  concern. 

859.  Nominal  Partners  are  those  whose  names  appear  in 
the  firm  title,  but  who  do  not  share  in  the  profits  of  the  business. 

860.  The  Net  Gain  or  Net  Loss  is  the  difference  between 
the  total  gain  and  the  total  loss. 


PARTNERSHIP  247 

861.  Pour  Cases  are  possible  in  finding  the  loss  or  gain  of 
the  several  partners,  viz  : 

CASE  I.  When  the  investments  of  each  partner  are  equal  and 
the  periods  of  investment  are  the  same,  the  losses  or  gains  should 
be  divided  equally. 

EXAMPLE  :  A  and  B  each  invest  $2500  for  2  years  and  gain  $4000. 
The  shares  of  the  gain  should  be  equal,  or  $2000  each. 

CASE  II.  When  the  investments  are  equal  and  the  periods  of 
investment  are  different,  the  losses  or  gains  should  be  divided  in 
proportion  to  the  periods  of  investment. 

EXAMPLE  :  A  invests  $2500  for  three  years,  and  B  invests  $2500  for  1 
year,  and  their  gain  is  $4000.  A  should  receive  $3000  and  B  $1000. 

CASE  III.  When  the  investments  are  unequal  and  the  periods 
of  investment  are  the  same,  the  profits  or  losses  shouid  be  divid- 
ed in  proportion  to  the  investments. 

EXAMPLE:  A  invests  $1500  for  2  years,  and  B  invests  $2500  for  2 
years,  and  the  gain  is  $2000.  A's  share  of  the  gain  should  be  f  of 
$2000,  or  $750,  and  B's  share  should  be  £  of  $2000,  or  $1250. 

CASE  IV.  When  both  investments  and  periods  of  investment 
are  different,  the  losses  or  gains  should  be  divided  in  proportion 
to  the  products  of  the  periods  and  the  investments. 

EXAMPLE  :  A  invests  $1500  for  2  years,  and  B  invests  $2500  for  4 
years,  and  their  gain  is  $2600. 

A's  $1500  for  2  years  =    $3000  for  1  year. 

B's  $2500  for  4  years  =_  10000  for  1  year. 

A's  and  B's  =  $13000  for  1  year. 

A's  share  is  T\  of  $2600,  or  $600. 

B's  share  is  \\  of  $2600,  or  $2000. 

NOTE — Salaries  of  partners  may  be  allowed,  and  interest  given  and 
received  on  deficiency  or  surplus  of  stated  capital  furnished,  and  the 
profits  or  losses  shared  according  to  special  agreement. 


PRACTICAL,  PROBLEMS 
862.     Solve  the  following  : 

1.  A  invests  $5000  ;  B,  $4000  ;    C,   $2000.     If  their  gain  is 
$2200,  what  is  the  share  of  each  ? 

2.  Jan.  1,  1907,  A  puts  in  $1500  ;   Mar.  1,  B  puts  in  $2000; 
June  1,  C  puts  in  $2500.     At  the  end  of  the  year  the  total  gain 
is  $1665.     What  is  the  share  of  each  ? 


248  MODERN  BUSINESS  ARITHMETIC 

3.  Brown,  Green,  and  Black  each  invest  $2000  in  a  property 
that  rents  for  $1200  per  year.     If  Brown  sells  out  to  Green  at 
the  end  of  six  months,  what  should  be  the  share  of  each  in  the 
year's  income? 

4.  A,  B,  C,  and  D  invest  in  a  manufacturing  plant.     At  the 
close  of  the  year,  A's  share  of  the  gain  was  $3240  ;   B's,  $2700  ; 
C's,  $2430,  and  D's,  $1890.     What  was  the  investment  of  each, 
if.  the  total  capital  was  $38000  ? 

5.  Adams,  Brown,   and  Cook  formed  a  partnership  Jan.   1, 
1908,    and    invested    and  withdrew  as  follows:     Jan.   1,   1908, 
Adams  invested  $800 ;  Brown  invested  $600,  and  Cook  invested 
$400.     April  1,  Adams  invested  $1000;  July  1,   $400,   and  Oct. 
1,    withdrew    $500.     May  1,   Brown  invested  $1200;    Sept.    1, 
$600,    and    Nov.    1,   withdrew  $1000.     June   1,   Cook  invested 
$400;  Aug.  1,  $400;   Oct.  1,  $400;   Dec.  1,  $400.     If  their  total 
gain  is  $2395,  what  should  be  the  share  of  each  partner  ? 


HOME  WORK— (Final) 

1.  Kelch,  Mize,  and  Holmes  were  associated  in  business  for 
3  years.     Kelch   invested  $8000;    Mize,   $10000,   and  Holmes, 
$12000.     They  agreed  to  organize  on  a  basis  of  $10000  each,  and 
to  pay  6%  interest  on  deficiencies,   and  accept  6%   interest  on 
surplus.     At  the  beginning  of  the  second  year,  Kelch  puts  in 
$3000  ;   Mize,  $2000',  and  Holmes,  $5000.     At  the  beginning  of 
the  third  year  Kelch  puts  in  $2000 ;   Mize,   $1000,   and  Holmes 
draws  out  $10'000.     If  the  total  gain  of  the  firm  is  $4980,  what 
is  the  present  worth  of  each  partner  at  the  end  of  3  years  ? 

2.  Wheeler,  Wyckoff,  and  Willis  are  partners.     Wheeler  in- 
vested $2000  in  cash  and  $4500  in  merchandise.     Wyckoff  in- 
vested a  note  for  $6000  due  in  one  year  with  interest  at  8  % ,  and 
cash,  $1000.     Willis  invested  merchandise  valued  at  $5000  and 
furnished  the  store  building  for  which  he  was  to  receive  $75  per 
month  rent.     Wheeler's  salary  as  manager  was  $1500,  Wyckoff  s 
$1200,  and  Willis's  $1000  per  year.     After  all  expenses  were 
paid  they  agreed  to  share  the  gains  or  bear  the  losses  equally. 
Find  the  present  worth  of  each  partner  at  the  end  of  the  year  if 
the  total  gain  was  $10030. 


PARTNERSHIP  249 

3.  Snow    invests    as   follows:     Cash,   $1200;     Merchandise, 
$2200:    Bills  Receivable,   $840;    Bank  Stock,   $1000;    Interest 
Receivable,  $260,  and  is  to  receive  $600  per  year  salary.     Frost 
invests :     Cash,  $500 ;  Store  and  Fixtures,  $3000,  subject  to  a 
mortgage  of  $1000  at  6%   interest;  Merchandise,  $1800;  Notes 
Receivable,  $1300;  Accounts  Receivable  valued  at  $1250,  sub- 
ject to  a  20%  discount  for  bad  debts  ;  and  is  to  receive  a  salary 
of  $800.     They  agree  that  the  one  investing  the  least  amount  of 
capital  shall  pay  the  other  6%  on  one-half  his  surplus.     Find 
the  present  worth  of  each  at  the  end  of  the  year,  if  the  total 
gain  of  the  business  is  $3800  and  they  divide  the  net  gain  equally. 

4.  R.  L,.  and  L.   S.  Goodyear  are  partners  under  the  firm 
name  of  Goodyear  Bros.,  and  are  dealers  in  rubber  materials  of 
all  kinds.     R.  L,.  invests  $12000,  cash,  and  L.  S.  invests  the  en- 
tire contents  of  his  store,   valued  at  $10000.     They  agree  that 
each  partner  shall  receive  7%  per  annum  on  his  investment,  and 
that  all  withdrawals  in  excess  of  $100  per  month  salary  shall 
be  charged  to  private  account  of  the  partner  withdrawing  the 
same.     At  the  end  of  the  year,  their  statement  is  as  follows : 
Merchandise  sales,   $78450  ;   Merchandise  purchases,    including 
original  stock,  $87300  ;   Merchandise  on  hand,  $15550  ;  Sundries 
losses,    $320 ;    Expenses,    not  including  salaries,    $750.     R.  L,. 
Goodyear  has  $580,  and  L,.  S.  Goodyear  has  $340  charged  to  his 
account.     Find  the  net  gain,  which  is  divided  equally,  and  pres- 
ent worth  of  each  partner  at  the  end  of  the  year. 

5.  Heald  and  Ingram  form  a  co-partnership.     Heald  invests 
store  and  lot,  $22000,  subject  to  a  mortgage  of  $7000  bearing 
6%  interest;   accounts  against  H.  E.  Cox  for  $2400,  J.   H.  Jan- 
son  for  $1525.75,  and   H.   L.   Gunn  for  $834.40;    Cash  $1840. 
He  also  owes  W.  E.  Gibson  on  account,  $524.50,  and  an  unpaid 
note  in  favor  of  First  National  Bank  for  $6000  bearing  7  %   int- 
erest, on  which  there  is  accrued  interest,  $75.65,  which  liabili- 
ties the  firm  assumes.     Ingram  invests  Merchandise,  $8425.60; 
Notes  Receivable,  $3271.90,  on  which  there  is  $148.20  accrued 
interest;  accounts  against  O.  B.  Parkinson  for  $380.40,   Edw'd 
Howe  for  $1135.50,  J.  R.  Humphreys  for  $576.75,   and  L.  W. 
Zinn  $650  ;    and  cash  sufficient  to  equalize  their  investments. 


250  MODERN  BUSINESS  ARITHMETIC 

Before  opening  the  store  for  business,  L,.  A.  Jordon  offers  to  buy 
a  one-third  interest  in  the  firm  by  giving  to  each  of  the  partners 
his  note  for  a  sufficient  sum  to  equalize  their  investments,  which 
offer  is  accepted.  At  the  end  of  the  year  the  sales  of  Merchan- 
dise amounted  to  $135420,  the  purchases  were  $142375.50,  and 
the  inventory  of  goods  on  hand  was  $23245.60.  After  paying 
running  expenses  $1245,  interest  on  mortgage  and  on  note  held 
by  the  First  National  Bank,  what  was  each  partner's  present 
worth  at  the  end  of  the  year  ? 


ANSWERS 


Article  49 

3. 

$1806 

Article  163 

1. 

2. 
3. 
4. 
5. 
6. 

$5155.11 
231851  mi. 
$41135.60 
751045  ft. 
7373736# 
$543811.50 

4. 
5. 
6. 
7. 

8. 

$2668 
$435    $315 
13  boxes 
$1408  A's 
$704  B's 
$352  C's 
706  acres 

1. 
2. 
3. 
4. 
5. 
6. 

217i  yds. 
672-j^  acres 
226J  yds. 
16J  and  11| 

9. 

205000 

7. 

$130} 

Article  50 

10. 

$208 

8. 

$3785^jj- 

1. 
2. 
3. 

$161416.75 
$92774.50  ' 

$148198.84 

1. 

Article  129 

72 

9. 

10. 

$1009| 
$277HB's 
$3845|  C's 
$8962|  total 

. 
5. 

$5480316.50 

2. 

3. 

1056 
12 

11. 
12. 

$3§ 

4 

1785 

13. 

tfggJL. 

Article  64 

5. 

-L  1  O*-J 

13ft. 

14. 

$151646A 

1. 

$5881.30 

5892 

15. 

$725iJ 

2. 

$9580.95 

6. 

$227.50 

3. 

$1028.50 

7. 

$126 

Article  174 

4. 
5. 

$6494 
$2800.50 

8. 
9. 

5    9     11 
140  ft. 
3696  gal. 

1. 
2. 

$2100     $2800 
$9600 

Article  95 

10. 

57  gal. 
37     59     67 

3. 
4. 

$1500 
Vs  of  estate 

1. 

$5330 

5. 

$420  Jones 

2. 
3. 

$155.66 
$93.75 

Article  131 

$1260  Brown 
$3150  Green 

4. 

$7198.75 

1. 

11  tons 

6. 

$600 

5. 

$8  1.25  lost 

2. 

64  brls. 

7. 

$3600 

6. 

$29103.75 

3. 

13  crates 

8. 

$240  Muir 

7. 

$382.44 

4. 

$2.80 

$320  Nunn 

8. 

$4500 

'  5. 

144  bu. 

$360  Hakes 

9. 

$61766 

6. 

160  bu. 

9. 

46%  doz. 

10. 

$264.60 

7. 

7  chests 

10. 

$16080 

8. 

49  yrs.     98  yrs. 

$6432  shoes 

Article  107 

9. 
10. 

50  yds. 

$3920  groceries 

$2880  tea 

1. 

580 

100  yds. 

$2260  hay 

2. 

$115 

200  yds. 

252 


MODERN  BUSINESS  ARITHMETIC 


Article  198 

3.     $67.50 

Article  251 

1.     196  acres 

4.     10i  ds. 
50  j 

1.     3p.m. 

2.     789.  15  chains 
3.     339.05  acres 
4.     $922.92} 
5.     606.  66i  acres 

d  as. 

6.     6  weeks 
7.     2|  ds. 
8.     2976  mi. 

9f\ 

2.     4  a.  m. 
3.     6  p.  m. 
4.     4:48  p.  m. 
5.     9  a.  m. 

6.     $70.43| 
7.     107  bu. 

y  men 
10.     16200  Ibs. 

Article  252 

8.     135  Ibs. 

9.     309  bu. 

Article  248 

1.     55 

10.     330.925  mi. 

1.     32  marbles 

2dtO 

2.     5i5T  past  1 
3.     27  1\  past  5 

Article  222 

1.     $290.94 

5M 
3.     $100 
4.     $4.95 

4.     49  iV  past  3 
5.     21T9T  past  4 

2.     $535.75 
3.     $3220.39 

5.     $39.60 
6.     81 

Article  253 

4.     $1595.35 

7.     15  yrs. 

1.     72  in. 

5.     1951.20 

8.     14  and  21 

2.     54  in. 

9.     I 

3.     80  ft. 

Article  224 

10.     360  ft. 

4!     32  ft! 

1.     $183.80 

5.     120  ft. 

2.     $724 

Article  249 

3.     $750 
4.     $4468.75 
5.     1  10  bu.  barley 
220  bu.  wheat 
440  bu.  corn. 

r.     $60  A's 
$150  B's 
2.     $210  A's 
$280  B's 

Article  254 

1.     16  yrs. 
2.     16  yrs.      36  yrs. 
3.     42  yrs.     70  yrs. 

$350  C's 

4.     5  yrs.        15  yrs. 

Article  232 

3.     $135  Jones 
$144  Brown 

5.     18  yrs.      36  yrs. 

1.     $51.98 
2.     $412.65 

$126  Smith 
4.     $294  White 

Article  255 

3.     $49.28 

$336  Green 

1.     25^  A 

4.     $705.30 

$140  Black 

10^  B 

5.     $582.25 

5.     $140      3  mo. 

2.     40  mi. 

6.     $614.80 
7.     $1144.50 

$900 

3.     300  yds. 
4.     $135 

8.     $1006.21 
9.     $983.25 

Article  250 

5.     $5.09|  A 
$2.90f  B 

10.     $537.86 

1.     Ifds. 

Article  247 

2.     2|  ds. 
3.     37i  ds. 

Article  381 

1.     $132 

4.     7i  ds. 

1.     1027s. 

2.     $27 

5.     21  ds. 

2.     13958  far. 

ANSWERS 


253 


3. 

£3  Id. 

6. 

$864 

5. 

14  bbls.  4  gal.  3 

4. 

45164  far. 

7. 

$3220 

qt.  1  pt.  3  gi. 

5. 

/3S  19s.  8d.  If. 

8. 

$55.38 

6. 

33|  bbls. 

6. 

lOOd. 

9. 

16800# 

7. 

240  bottles 

7. 

696  far. 

336  bu.  barley 

8. 

144  bottles 

8. 

/3  10s.  5d.  3  f. 

300  bu.  flaxseed 

9. 

$33 

9. 

$245.88 

280  bu.  wheat 

10. 

90^ 

10. 

^1172   10s. 

525  bu.  oats 

10. 

$945 

Article  388 

Article  382 

Article  385 

1. 

f  3  7904 

1. 

32.4  francs 

2. 

IH26385 

2. 

4200  centimes 

1. 

357  drams. 

3. 

mll09315 

3. 

$409.74 

2. 

9355  gr. 

4. 

O5f5lOf34ml6 

4. 
5. 

11000  fr. 
5043.05  fr. 

3. 
4. 

58  56  92  gr.5 
43  Ibs.  57  3292 

5. 

Cong.  15   07 
f5l5  f36 

6. 

42.8  marks 

5. 

280  capsules 

6. 

1408  bottles 

7. 

7500  pf  . 

6. 

3  Ibs.  37  36 

7. 

Cong.  23  O2 

8. 

$62.13 

7. 

$43.75 

8. 

$1.05 

9. 

11000  marks 

8. 

$184.80 

9. 

$44 

10. 

386  marks 

9. 

4800  doses 

10. 

4032  bottles 

10. 

$52.68 

Article  383 

Article  386 

Article  389 

'1. 

1340  pwt. 

1 

8-A-  1h<; 

1. 

189  qts. 

2. 

3. 
4. 
5. 

19570  gr. 
98374  gr. 
12  oz. 
37  Ibs. 

_L  . 

2. 
3. 
4. 

°3lT  -lus. 

12H  Ibs. 
12  Ibs.  51  36  92 
10  Ibs.    105    43 

1  rv   ~ 

2. 
3. 
4. 

5. 

1111  pts. 
1102  pts. 
2bu. 
900  bu.   1  pk.   7 

6. 

7. 
8. 
9. 
10. 

6  Ib.  1  oz.  5  pwt. 
19  gr. 
$14 
40  spoons 

$85 
$1189.02 

5. 
6. 

7. 
8. 

10  gr. 
21  Ibs.   6  oz.   16 
pwt.  26  gr. 
Feathers 
1240  gr. 
Gold     42^  gr. 
Lost  $106.25 

6. 
7. 
8. 
9. 
10. 

qt.  1  pt. 

$11.52 
$3 
18  bu. 

$5.72 
$4.65 

9. 

$85.83 

Article  384 

10. 

$5.17      $6.20 

Article  390 

1. 
2. 

9212  oz. 
5648  Ibs. 

Article  387 

1. 
2. 

1795  in. 
67082.4  in. 

3. 

1.6  cwt. 

1. 

47  pts. 

3. 

942636  in. 

4. 

18  T.  7  cwt.  28 

2. 

3745  gi. 

4. 

1  mi.  1  fur.  2  yd. 

Ibs.  2  oz. 

3. 

8964  gi. 

1  ft. 

5. 

13  T. 

4. 

9  bbls. 

5. 

4  mi.  38  ch.  241. 

254 


MODERN  BUSINESS  ARITHMETIC 


6.     $11200 

Article  394 

Article  410 

7.     10725  ft. 

8.     2610  mi. 

1. 

4545  ds. 

1. 

1  hr.  6  min.  17 

9.     $382.80 

2. 

72740  min. 

sec. 

10.     306662.4  times 

3. 

67  ds.  12  hrs. 

2. 

51min.32if  sec. 

4. 

15  ds.  12  hr.  59 

3. 

8  hr.  58  min.  14 

Article  391 

5. 

min.  42  sec. 
41760  min. 

4. 

sec.  a.  m. 
5  hrs.  9  min. 

1.     7128  sq.  in. 

6. 

86400  sec. 

56i  sec.  p.  m. 

2.     59553  sq.  yd. 

7. 

161  ds. 

5. 

10  hrs.  12  min. 

3.     104684  sq.  ft. 

8. 

129600  times 

25  sec  a.  m. 

4.     11  sq.  yd.  29  sq 

.  9. 

2  yrs.  6  mo.  18 

6. 

121°  30'  15" 

in. 

ds. 

7. 

East 

5.     45.21875  acres 

10. 

6  mo.  10  ds. 

23°  11'    15" 

6.     $1642.67 

8. 

East,  Cincinnati 

7.     $240 
8.    $177.78 

Article  395 

9. 

8  hr.  36  min.  56 
sec.,  or  15  hr. 

9.     $6050 

1. 

26670" 

23  min.  4  sec. 

10.     $452.60 

2. 

165054" 

10. 

Gain  10  hr.  58 

3. 

358°  5' 

min.  37  sec. 

Article  392 

4. 

127°  11'  4" 

Also  one  whole  day 
in  calendar  caused  by 

1.     2560  acres 

5. 
6. 

10028.  2  mi. 
2665180  sec. 

crossing  the   Interna- 
tional Date  Line. 

2.     10  acres 
3.     257500  sq.  1. 

7. 

2903|  mi. 

A  r\Q 

Article  413 

4.     1  sq.  ch.  11  sq. 
rd.  467  sq.  1. 
5.     360  sq.  ch. 

8. 
9. 
10. 

40 
24897.6  mi 
66°  7'  30" 

1. 
2. 
3. 

5s.  7d.  2  far. 
7s.  4d.  2  far. 
3  yd.  7-J  in. 

6.     64|  acres  , 
7.     40  acres 

Article  396 

4. 

1  fur.   38  rds.   2 
yds.  7.2  in. 

8.     $2800 
9.     $10000 

1. 

$43.20 

5. 

6  oz.  10  pwt.  12 
gr. 

10.     $156.25 

2. 

$36 

6. 

7  cwt.  30  Ib.  12 

3. 

$6.375 

oz. 

Article  393 

4. 

40  yrs.  A 

7. 

240  acres 

1.     29508  cu.  in. 

60  yrs.  B 

8. 

14  gi. 

fU.-4       r\  ** 

2.     697  cu.'ft. 
3.     1536  cu.  ft. 

5. 

20  yrs.  C 
36  yrs.  James 

9. 

10. 

$1.2o 
1234.5  sq.  links 

4.     30  cu.  ft. 
5.     497664  cu.  in. 

6. 

48  yrs.  Henry 
960  sheets 

Article  415 

6.     $76.80 

7. 

$27 

1. 

iV  gal. 

7.     9  cords 

8. 

$1.92 

2. 

A  yd. 

8.     $39.27 

9. 

10000  sheets 

3. 

Tib  bu. 

9.     123354  bricks 

10. 

5000  booklets 

4. 

•yj*  mi. 

10.     $84270 

16  pp.  each 

5. 

.0225  ton 

ANSWERS 


255 


6. 

.0075  ds. 

3. 

174  gal.  2  qt. 

3. 

32206.30^  sq, 

.ft. 

7. 

leu  mark 

4. 

5752  bu.  2  pk. 

4. 

50.93  acres. 

8. 

J6.016J 

5. 

$75.26 

5. 

12880.56  sq. 

ft. 

9. 

A 

10. 

12  yrs.      27  yrs. 

Article  428 

Article  468 

Article  417 

1. 

35  A  90  sq.  rds. 

1. 

624  sq.  ft. 

1. 

•«rd. 

9   sq.   yds.    6 
sq.  ft.   57  sq. 

2. 
3. 

263.9  sq.  in. 
3.1416sq.  ft, 

2. 

.8775  cwt. 

in. 

4. 

706.86  sq.  in 

3. 

.671875  bu. 

2. 

£5   11s.    Id.     1 

5. 

$14137.20 

4. 

.3125  sq.  yd. 

far. 

5. 
6. 

H 

i  hhd. 

3. 

7  gal.  2  qt.  1  pt. 
if  gi. 

Article  480 

7. 

vo^B 

4. 

243  bxs. 

1. 

48  cu.  ft. 

8. 

.0325  cwt. 

5. 

150  farms 

2. 

35937  cu.  in. 

9. 

.05009375 

3. 

1331  cu.  in. 

10. 

.6375 

Article  457 

4. 
5. 

216  gal. 
384  bu. 

Article  420 

1. 

116}  sq.  rds. 

1. 

20  cwt.  2  Ib.  14 

2. 

850  sq.  ft. 

Article  482 

.2. 

oz. 
11  da.  23  min.  5 
sec. 

3. 

4. 

5. 

31  sq  yd. 
316  sq.  yd. 
1100  sq.  yd. 

1. 

2. 

100  cu.  ft. 
16200  cu.  ft. 
$5103 

3. 
4. 

27  yd.  1  ft. 
3  hhd.  1  bbl.  23 

Article  459 

3. 
4. 

$4640 
150  cu.  in. 

5. 

gal.  1  pt.  1  gi. 
29  Ib.  35  53   11 

1. 
2. 

102  sq.  ft. 
400  sq.  ft. 

5. 

11309.76  cu. 

in. 

gr. 

3. 

80  sq.  ft. 

Article  484 

Article  423 

4. 
5. 

2}|  acres 

$14832.28 

1. 

75  cu.  ft. 

1. 

10  rd.  3yd.  2ft. 

2. 

20800  cu.  ft. 

2  in. 

Article  461 

3. 

2261.  952  cu. 

ft. 

2. 
3. 

3  pk.  2  qt.  |  pt. 
25  cd.   5  cd.   ft. 

1. 

336  sq.  ft. 

4. 
5. 

9629-B  cu.  ft. 
93i  board  ft. 

12  cu.  ft. 

2. 

147  sq.  ft. 

4. 

5. 

31  gal.  3  gi. 
135  A   4  sq.  ch. 

3. 
4. 
5. 

125  A 

682  sq.  ft. 
378  sq.  ft. 

1. 

Article  485 

33.5104  cu  in 

Article  427 

2. 

523.6  cu.  ft. 

Article  463 

3. 

65.45  cu.  in. 

1. 

1  mi.  3  rd.  1  yd. 

4. 

268,083,200,000 

1  ft.  8  in. 

1. 

7854  sq.  ft. 

cu.  mi. 

2. 

44  bu.  5  qt. 

2. 

314.16sq.  yd. 

5. 

202.  1096  cu. 

in. 

256 


MODERN  BUSINESS  ARITHMETIC 


Article  486 


Article  504 


1.      16  tons 

1.     186.01  bu. 

2.      108  sq.  rd. 

2.     3456  bu. 

3.      16  Ibs. 

3.     3  ft.  2  in. 

4.     6f  hrs. 

4.     10  ft.  3  in. 

5.     259i  Ibs. 

5.     $1440 

Article  489 

6.     628T4T  gal. 
7.     68.39  bbls. 

1.     $24.60 

8.     270  gal. 

2.     $30.49 

9.     50.49  bbls. 

3.     $80.75 

10.     20  ft. 

4.     $92.11 

5.     $74.08 

Article  513 

6.     $68.04 

1          R       Q 

7.     $139.01 

X  •          U         O 

9         3fi 

8.     $28.33 

£  .         OU 

1        1 

9.     $40 

O.         9 
4.         Q 

10.     $363.33  or 
$356.53  by  cut- 

T-.        t/ 

5.     245 
6      10 

ting  strips 

7:     It 

Article  494 

8.     21J 

1.     $51 

10          TTT 

2.     $40.50 

*v«         go 

3.     8280  bricks 
4.     $131.71 

Article  521 

5.     $269.64 

1.     30 

6.     $86.40 

2.     30 

7.     $57.82 

3.     84 

8.     $112.48 

4.     76 

9.     $466.22 

5.     8 

10.     $836.14 

6.     119  Ibs. 

Article  499 

7.     5f  bu. 
8.     4  ds. 

1.     4-I-,  cords 

9.     2  men 

2.     7*  cords 

10.     20  men 

3.     134  ft. 

4.     560  ft. 

Article  525 

5.     25i  feet 

6.     $408.24 

1.     $4.50 

7.     $121.50 

2.     96  horses 

8.     $219.28 

3.     96  sheep 

9.     $198 

4.     $47.50 

10.     26280  shingles 

5.     8  mo. 

6.  220  rods 

7.  1600  books 

8.  21504  bricks 

9.  10  men 

10.  8  men 

Article  543 

1.  $21     108  Ibs. 

2.  180  bu. 
280  tons 

3.  117  hrs.     $259 

4.  $129J- 

5.  $2700 

6.  $4140 

7.  $800 

8.  $2250 

9.  $625 
10.  $18000 

Article  545 

1.  50%     25% 

2.  24%     20% 

3.  400%     300% 

4.  80%     90% 
5. 

6. 
7. 

8.  $1584     32% 

9.  20% 
10.  75% 

Article  547 

1.  576    429 

2.  $2520    $1372 

3.  192  ft. 

4.  $1101.82 

5.  $7500 

6.  $355 

7.  $1500 

8.  $50000 

9.  42  gal. 

10.  700  head 


ANSWERS 


257 


Article  549 

1.  80    96 

2.  $200    $360 

3.  546  sheep 

4.  75  marbles 

5.  $800 

6.  $13500 

7.  700  acres 

8.  $570 

9.  $35 
10.  11000 


1. 

2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 


Article  559 

$100 

15^  per  bu. 

$250 

$240.63 

$208.25 

$54 

$1875 

$2385 

$39.90 

$1745.05 

Article  561 


1.  25% 

2.  25% 

3.  18% 

4.  43  J% 

5.  30% 

6.  1U% 

7.  25% 

8.  47H% 

9.  20% 
10.  100% 

Article  563 

1.  $50 

2.  $700 

3.  $3240 

4.  $1960 

5.  $4900 


6.     $20 

5.     $2225 

7.     $1927.50 

6.     $24 

8.     $270 

7.     $437.50 

9.     $2000 

8.     $580 

10.     $100000 

9.     18|% 

10.     16% 

Article  565 

Article  600 

1.     $25 
2.     $336 
3.     $1333i 
4.     $106.66f 
5.     $1480 
6.     $560 
7       ftfi 

1.     $36 
2.     $106.50 
3.     $57.50 
4.     $1347.84 
5.     $152.77 
6.     $425.36 

/  .         fl5U 

8.     $32  lost 
9.     $2835 
10.     60% 

7.     $3229.20 

8.     $876.02 
9.     $422.60 
10.     $1872 

Article  576 

Article  602 

1.     $375 

1.     2% 

2.     $735 

2.     6% 

3.     $900 

3.     2i% 

4.     $2700 

4.     124% 

5.     $540 

5.     2f% 

6.     $1120 

6.     3% 

7.     $576 

7.     5% 

$480 

8.     4% 

$432 

9.     4i% 

$384 

10.     6%     $212 

$288 

8.     $1157.62 

Article  604 

9.     $495.72,  8  ds. 

$523.26,  20  ds. 

1.     $7000 

$550.80,  40  ds. 

2.     $4940 

10.     50,  20,   and   10, 

3.     $223.10 

better  by  l\  % 

4.     $1420 

5.     $1450 

Article  579 

6.     $2569.75 
$3208.40 

1.     $350 

7.     $601.60 

2.     $735 

8.     $692.23 

3.     $840 

9.     48225  Ibs. 

4.     $1337.50 

10.     $2850 

258 


MODERN  BUSINESS  ARITHMETIC 


Article  606 

4.     6J% 

6.     $1750 

5.     120  shares 

7.     $1485240 

1.     $540 
2.     $17240 

6.     $7515 
7.     6's  at  120, 

8.     $209.50 
.0115+ 

3.     $922.40 

$180 

9.     $859.04 

4.     $20.70 

8.     $195  increase 

10.     $10000 

5.     $12560 
6.     $1973.79 
7.     $32.  85  gain 
8.     1550  Ibs. 
9.     204347#  Island 
235600#  Ala. 

$82.75  surplus 
9.     $4  decrease 
$8.75  surplus 
10.     $17820  Mich.  6 
$35640  Ohio  5' 

Article  696 

's  1.     $58.10 
s    2.     $173.84 
3.     $152.10 

10.     $5200    $4750 

Article  651 

4.     540.76 

5.     $2160 

Article  634 

1.     $160200 

6.     $3082 

ffaf*  S\  f\ 

2.     $325000 

7.     $246 

1  .     $600 
2.     $20.50 
3.     $1024 
4.     $392 
5.     $4500    $75 
6.     $345 
7.     $8352 

3.     $36800 
4.     $189 
5.     $45.80 
6.     $209.75 
7.     $562400 
8.     $385952.85 
9.     $126.40 

8.     27  yrs. 
9.     $2000 
10.     '65  yrs. 

Article  713 

1.     $.1725 

8.     $308 

2.     $37.60 

9.     $560 
10.     $5500    $495 

Article  669 

3.     $243.38 

4.     $187.68 

1.     $460 

5.     $448.25 

Article  636 

2.     $974.50 

6.     $782.25 

3.     $128 

7.     $2660.97 

2-|    -t    /T/ 

4.     $604.45 

8.     $825.84 

.       11% 

31  rrt 

5.     $2394.33 

9.     $574.56 

.       i% 

6.     $17374.85 

10.     $1125.25 

4.     4-|% 

51     /7^ 

7.     20% 

•         8% 

6.     8}% 
7.     7%     $3750 

8.     $4151.66 
9.     $1116 
10.     $2160 

Article  719 

1.     $1.88 

8.     15J% 
9.     12%     $1210.68 

$4320 

2.     $.79 
3.     $11.09 

10.     7% 

Article  686 

4.     $32.50 

—             .ji/irr    ^7O 

5.     $67.73 

Article  638 

1.     $15 

6.     $5.27 

2.     $37.50 

7.     $3.97 

1.     320  shares 

3.     $31.50 

8.     $11.97 

2.     $29835 

4.     $1928 

9.     $45.79 

3.     $8883.75 

5.     $4500 

10.     $2.56 

ANSWERS 


259 


Article  721 

4.      $672 

10.     $764.19 

1.     $37500 
2.     $720 
3.     $1200 
4.     $540 

5.     $280 

5.     $4050 
6.     $1277.50 
7.     $2250 
8.     $4800 
9.     $7500 

Article  776' 

1.     $878.04 
2.     $1270.89 

6.     $600 

10.     $12000 

3.     $455.77 

7.     $1200 

4.     $2124.83 

8.     $500 

Article  732 

5.     $651.17 

9.     $19500 
10.     $24003 

1.     $3.96 
2.     $8.82 

6.     $587.26 
7.     $3513.60 
8.     $2701.22 

Article  723 

3.     $2.88 
4.     $8.47 

9.     $1107.17 
10.     $1006.72 

1.     6% 

5.     $7.40 

2.     8% 
3.     8% 

6.     $32.55 
7.     $26.04 

Article  783 

4.     8% 

8.     $81 

1.     $711.55 

5.     1% 

9.     $160.80 

2.     $1376.08 

6.     8% 

10.     $28.80 

3.     $303.27 

7.     8% 

4.     $568.87 

8.     4^% 

Article  737 

5.     $363.85 

9      4% 

^  •          ^r  /€/ 

10.     7|% 

1.     $268.92 

Article  784 

2.     $543 

Article  725 

3.     $422.03 
4.     $1335.36 

1.     $701.80 
2.     $122.44 

1.     8  mo. 

5.     $101.76 

3.     $67.48 

2.     77  ds. 

6.     $164.56 

4.     $117 

3.     45  ds. 

7.     $931.35 

5.     $216.10 

4.     7  mo.  6  ds. 

8.     $35.28 

5.     4  mo.  21  ds. 

9.     $465 

Article  799 

6.     1  yr.    3  mo.    15 

10.     $1058.83 

ds. 

1.     $240 

7.     lyr.  5  mo.  3  ds. 

Article  742 

2.     $9.90 

8.     2  yr.    3  mo.    18 
ds. 

1.     $74.16 

3.     $11.40 
4.     $1045.35 

9.     312  ds. 

2.     $262.48 

5.     $2.36 

10.     6  mo. 

3.     $704.25 

6.     Cash  discount 

4.     $1256.86 

$3.78 

Article  727 

5.     $238.91 
6.     $2088.44 

7.     Let  bill  run 
$52.50 

1.     $240 

7.     $4850.45 

8.     $3016.76 

2.     $310 

8.     $129.76 

9.     $924 

3.     $436.20 

9.     $311.64 

10.     $5342 

MODERN  BUSINESS  ARITHMETIC 


Article  819 

6. 

In  2  mo. 

4.     $1814.80  gain 

1. 

$3.11 

7. 

7  mo.  24  ds.  after 

5.     $8909.65 

2. 
3. 
4. 

5. 

$760.95 
$7329.15 
$256 
$2929.31 

8. 
9. 

Feb.  1,  or  on 
Sept.  25th. 
66  ds.     Sept.  5 
88  ds.     Oct.  28, 

1  QH& 

Article  862 

1.     $1000  A 

6. 

7. 

$304 
$201.60 

10. 

•ItJUo 

$1677.58 

$800  B 
$400  C 

8. 

$732.54 

Article  835 

2.     $12000  A 

$5000 

$10000  B 

$1592.86 

1. 

July  7,  '07 

$9000  C 

9. 

$14334.52    13% 

2. 

June  18,  '08 

$7000  D 

$910.68 

3. 

Oct.  18,  '07 

3.     $200  Brown 

10. 

$2288.75 

4. 

Oct.  30,  '08 

$600  Green 

1. 

Article  832 

400  mo.     $200 

5. 

July  19,  '07 
Article  848 

$400  Black 
4.     $540  A 
$600  B 

2. 

2800  mo.      $400 

1. 

$5411.74 

$525  C 

3. 

6  mo. 

2. 

$545 

5.     $975  A 

4. 

$1400 

3. 

$21812.35 

$860  B 

5. 

3  mo. 

$2812.35 

$5600 

236567 


